Search

We study the computational complexity of (deterministic or randomized) algorithms based on point samples for approximating or integrating functions that can be well approximated by neural networks. Such algorithms (most prominently stochastic gradient descent and its variants) are used extensively in the field of deep learning. One of the most important problems in this field concerns the question of whether it is possible to realize theoretically provable neural network approximation rates by such algorithms. We answer this question in the negative by proving hardness results for the problems of approximation and integration on a novel class of neural network approximation spaces. In particular, our results confirm a conjectured and empirically observed theory-to-practice gap in deep learning. We complement our hardness results by showing that error bounds of a comparable order of convergence are (at least theoretically) achievable. [ABSTRACT FROM AUTHOR]

Minimizing the weighted completion time of jobs in the unrelated parallel machines model is a fundamental scheduling problem. The first (3 / 2 - c) –approximation algorithm for this problem, for some constant c > 0 , was obtained in the work of Bansal et al. (SIAM J Comput, 2021). A key ingredient in this work was the first dependent-rounding algorithm with a certain guaranteed amount of negative correlation. We improve upon this guaranteed amount from 1/108 to 1/27, thus also improving upon the constant c in the algorithms of Bansal et al. and Li (SIAM J Comput, 2020) for weighted completion time. Given the now-ubiquitous role played by dependent rounding in scheduling and combinatorial optimization, our improved dependent rounding is also of independent interest. [ABSTRACT FROM AUTHOR]

Variational Quantum Algorithms (VQAs) have made great success in the Noisy Intermediate-Scale Quantum (NISQ) era due to their relative resilience to noise and high flexibility relative to quantum resources. Quantum Architecture Search (QAS) aims to enhance the performance of VQAs by refining the structure of the adopted Parameterized Quantum Circuit (PQC). QAS is garnering increased attention owing to its automation, reduced reliance on expert experience, and its ability to achieve better performance while requiring fewer quantum gates than manually designed circuits. However, existing QAS algorithms optimize the structure from scratch for each VQA without using any prior experience, rendering the process inefficient and time-consuming. Moreover, determining the number of quantum gates, a crucial hyper-parameter in these algorithms is a challenging and time-consuming task. To mitigate these challenges, we accelerate the QAS algorithm via a meta-trained generator. The proposed algorithm directly generates high-performance circuits for a new VQA by utilizing a meta-trained Variational AutoEncoder (VAE). The number of quantum gates required in the designed circuit is automatically determined based on meta-knowledge learned from a variety of training tasks. Furthermore, we have developed a meta-predictor to filter out circuits with suboptimal performance, thereby accelerating the algorithm. Simulation results on variational quantum compiling and Quantum Approximation Optimization Algorithm (QAOA) demonstrate the superior performance of our method over a state-of-the-art algorithm, namely Differentiable Quantum Architecture Search (DQAS). [ABSTRACT FROM AUTHOR]

Personalized travel itinerary recommendation algorithms are the focus of research in smart tourism and tourism GIS. Aiming to address issues present in travel itinerary recommendations for the increasingly popular "self-drive tour" mode, this study proposes an algorithm based on comprehensive tourist satisfaction to mitigate problems such as the neglect of important relevant factors and low degree of personalization. First, we construct a model of tourist satisfaction for travel itineraries by comprehensively considering factors including time utilization, the attractiveness of attractions, itinerary feasibility, and the diversity of attraction types. Unlike previous studies, we consider dining and accommodation time during the itinerary, the physical condition of tourists, and the diversity of attraction types, and establish penalty functions to flexibly constrain deviations from the expected conditions in itinerary planning. Then, with the optimization of comprehensive tourist satisfaction as the objective, we design a new algorithm to address the itinerary recommendation problem, supporting tourists in selecting must-visit attractions, restaurants, and hotels, as well as personalized preferences such as the sightseeing sequence. The experimental results demonstrate that our proposed algorithm outperforms two baseline algorithms, providing higher comprehensive tourist satisfaction while also exhibiting greater feasibility in itinerary planning. The proposed algorithm effectively addresses the issue of personalized travel itinerary recommendation, presenting an efficient, feasible, and practical solution. [ABSTRACT FROM AUTHOR]

Graph coloring is the assignment of one color to each vertex of a graph so that two adjacent vertices are not of the same color. The graph coloring problem (GCP) is a matter of combinatorial optimization, and the goal of GCP is determining the chromatic number (G). Since GCP is an NP-hard problem, then in this paper, we propose a new approximated algorithm for finding the coloring number (it is an approximation of chromatic number) by using a graph adjacency matrix to colorize or separate a graph. To prove the correctness of the proposed algorithm, we implement it in MATLAB software, and for analysis in terms of solution and execution time, we compare our algorithm with some of the best existing algorithms that are already implemented in MATLAB software, and we present the results in tables of various graphs. Several available algorithms used the largest degree selection strategy, while our proposed algorithm uses the graph adjacency matrix to select the vertex that has the smallest degree for coloring. We provide some examples to compare the performance of our algorithm to other available methods. We make use of the Dolan-Moré performance profiles to assess the performance of the numerical algorithms, and demonstrate the efficiency of our proposed approach in comparison with some existing methods. [ABSTRACT FROM AUTHOR]

This paper studies a classic maximum entropy sampling problem (MESP), which aims to select the most informative principal submatrix of a prespecified size from a covariance matrix. MESP is widely applied to many areas, including healthcare, power systems, manufacturing, and data science. By investigating its Lagrangian dual and primal characterization, we derive a novel convex integer program for MESP and show that its continuous relaxation yields a near-optimal solution. The results motivate us to study efficient approximation algorithms and develop their approximation bounds for MESP, which improves the best known one in the literature. This paper studies a classic maximum entropy sampling problem (MESP), which aims to select the most informative principal submatrix of a prespecified size from a covariance matrix. By investigating its Lagrangian dual and primal characterization, we derive a novel convex integer program for MESP and show that its continuous relaxation yields a near-optimal solution. The results motivate us to develop a sampling algorithm and derive its approximation bound for MESP, which improves the best known bound in literature. We then provide an efficient deterministic implementation of the sampling algorithm with the same approximation bound. Besides, we investigate the widely used local search algorithm and prove its first known approximation bound for MESP. The proof techniques further inspire for us an efficient implementation of the local search algorithm. Our numerical experiments demonstrate that these approximation algorithms can efficiently solve medium-size and large-scale instances to near optimality. Finally, we extend the analyses to the A-optimal MESP, for which the objective is to minimize the trace of the inverse of the selected principal submatrix. Funding: This work was supported by the National Science Foundation Division of Information and Intelligent Systems [Grant 2246417] and Division of Civil, Mechanical and Manufacturing Innovation [Grant 2246414]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/opre.2023.2488. [ABSTRACT FROM AUTHOR]

Solving combinatorial problems on complex networks represents a primary issue which, on a large scale, requires the use of heuristics and approximate algorithms. Recently, neural methods have been proposed in this context to find feasible solutions for relevant computational problems over graphs. However, such methods have some drawbacks: (1) they use the same neural architecture for different combinatorial problems without introducing customizations that reflects the specificity of each problem; (2) they only use a nodes local information to compute the solution; (3) they do not take advantage of common heuristics or exact algorithms. Following this interest, in this research we address these three main points by designing a customized attention-based mechanism that uses both local and global information from the adjacency matrix to find approximate solutions for the Minimum Vertex Cover Problem. We evaluate our proposal with respect to a fast two-factor approximation algorithm and a widely adopted state-of-the-art heuristic both on synthetically generated instances and on benchmark graphs with different scales. Experimental results demonstrate that, on the one hand, the proposed methodology is able to outperform both the two-factor approximation algorithm and the heuristic on the test datasets, scaling even better than the heuristic with harder instances and, on the other hand, is able to provide a representation of the nodes which reflects the combinatorial structure of the problem. [ABSTRACT FROM AUTHOR]

Aiming to address problems such as low sampling success rate and long computation time in the motion planning of a dual-arm cooperative system with multiple constraints, this paper proposes an Informed-Bi-Quick RRT* algorithm based on offline sampling. First, in the process of pre-sampling, the new algorithm relaxes the approximation of constrained manifolds by introducing the idea of incremental construction, and it incorporates the stochastic gradient descent method to replace global random sampling with local random sampling, which enriches the data set and shortens the offline sampling time of the data set. Second, the new algorithm improves the original Quick-RRT* algorithm by combining the two-tree idea and the multi-target bias expansion strategy, and it improves the adaptability of the algorithm to different obstacle environments. In addition, the loosely constrained motion and tightly constrained motion in the two-arm cooperative system are analyzed, and the adaptive planning of the two-arm trajectory in different motions is described in detail. In this paper, the two-arm cooperative model constructed with UR5 and UR10 robot arms is studied, and the ability of the proposed algorithm to deal with multiple constraints is verified by simulating assembly and handling tasks. The experimental results show that compared with other methods, the proposed algorithm has obvious advantages in path quality and planning efficiency. [ABSTRACT FROM AUTHOR]

In "Sequential Competitive Facility Location: Exact and Approximate Algorithms," Qi et al. consider a competitive facility location problem (CFLP), where two firms sequentially open new facilities within their budgets and maximize their market shares of demand following a probabilistic choice model. They derive an equivalent, single-level mixed-integer nonlinear program (MINLP) reformulation of the bilevel MINLP and exploit the problem structures to derive valid inequalities based on submodularity and concave overestimation. They also develop an approximation algorithm with a constant approximation guarantee. They further study several extensions of CFLP that have general facility-opening costs, outside competitors, and diverse facility-planning decisions. Their approaches significantly accelerate the computation of CFLP on large-sized instances that have not been solved optimally or even heuristically by existing methods. We study a competitive facility location problem (CFLP), where two firms sequentially open new facilities within their budgets, in order to maximize their market shares of demand that follows a probabilistic choice model. This process is a Stackelberg game and admits a bilevel mixed-integer nonlinear program (MINLP) formulation. We derive an equivalent, single-level MINLP reformulation and exploit the problem structures to derive two valid inequalities based on submodularity and concave overestimation, respectively. We use the two valid inequalities in a branch-and-cut algorithm to find globally optimal solutions. Then, we propose an approximation algorithm to find good-quality solutions with a constant approximation guarantee. We develop several extensions by considering general facility-opening costs and outside competitors as well as diverse facility-planning decisions, and we discuss solution approaches for each extension. We conduct numerical studies to demonstrate that the exact algorithm significantly accelerates the computation of CFLP on large-sized instances that have not been solved optimally or even heuristically by existing methods, and the approximation algorithm can quickly find high-quality solutions. We derive managerial insights based on sensitivity analysis of different settings that affect customers' probabilistic choices and the ensuing demand. Funding: M. Qi was partially supported by the National Natural Science Foundation of China [Grant 71772100] to work on this project. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2022.2339. [ABSTRACT FROM AUTHOR]

Conceptual distance refers to the degree of proximity between two concepts within a conceptualization. It is closely related to semantic similarity and relationships, but its measurement strongly depends on the context of the given concepts. DIS-C represents an advancement in the computation of semantic similarity/relationships that is independent of the type of knowledge structure and semantic relations when generating a graph from a knowledge base (ontologies, semantic networks, and hierarchies, among others). This approach determines the semantic similarity between two indirectly connected concepts in an ontology by propagating local distances by applying an algorithm based on the All Pairs Shortest Path (APSP) problem. This process is implemented for each pair of concepts to establish the most effective and efficient paths to connect these concepts. The algorithm identifies the shortest path between concepts, which allows for an inference of the most relevant relationships between them. However, one of the critical issues with this process is computational complexity, combined with the design of APSP algorithms, such as Dijkstra, which is n 3 . This paper studies different alternatives to improve the DIS-C approach by adapting approximation algorithms, focusing on Dijkstra, pruned Dijkstra, and sketch-based methods, to compute the conceptual distance according to the need to scale DIS-C to analyze very large graphs; therefore, reducing the related computational complexity is critical. Tests were performed using different datasets to calculate the conceptual distance when using the original version of DIS-C and when using the influence area of nodes. In situations where time optimization is necessary for generating results, using the original DIS-C model is not the optimal method. Therefore, we propose a simplified version of DIS-C to calculate conceptual distances based on centrality estimation. The obtained results for the simple version of DIS-C indicated that the processing time decreased 2.381 times when compared to the original DIS-C version. Additionally, for both versions of DIS-C (normal and simple), the APSP algorithm decreased the computational cost when using a two-hop coverage-based approach. [ABSTRACT FROM AUTHOR]

We study several two-machine shop scheduling problems, namely flow shop, job shop and open shop scheduling problems under linear constraints. In these problems, the processing times of two stages of jobs are also decision variables and satisfy a system of linear constraints. The goal of each problem is to determine the processing time of each job, and to schedule the jobs to the shop machine such that the makespan, i.e., the completion time of all jobs, is minimized. These problems can find application in various areas, such as industrial production, advertising and automotive maintenance. We study the computational complexity and propose polynomial-time optimal or approximation algorithms for them. In particular, we show that although a two-machine flow shop scheduling problem and a two-machine job shop scheduling problem without recirculation can be solved in polynomial time, the problems where processing times satisfy linear constraints are generally NP-hard in the strong sense. Then, we design algorithms for various settings of these problems. We design polynomial-time algorithms for them when there are a fixed number of constraints. For the general case, we first propose a simple 2-approximation algorithm, and then design a polynomial-time approximation schemes. In contrast to the previous two problems, we show that the two-machine open shop scheduling problem under linear constraints can be solved in polynomial time. [ABSTRACT FROM AUTHOR]

We present improved algorithms for the Steiner tree problem with the minimum number of Steiner points and bounded edge length. Given n terminal points in a 2D Euclidean plane and an edge length bound, the problem asks to construct a spanning tree of n terminal points with minimal Steiner points such that every edge length of the spanning tree is within the given bound. This problem is known to be NP-hard and has practical applications such as relay node placements in wireless networks, wavelength-division multiplexing(WDM) optimal network design, and VLSI design. The best-known deterministic approximation algorithm has O(n3) running time with an approximation ratio of 3. This paper proposes an efficient approximation algorithm using the Voronoi diagram that guarantees an approximation ratio of 3 in O(n log n) time. We also present the first exact algorithm to find an optimal Steiner tree for given three terminal points in constant time. Using this exact algorithm, we improve the 3-approximation algorithm with better performance regarding the number of required Steiner points in O(n log n) time. [ABSTRACT FROM AUTHOR]

We study the investment incentives created by truthful mechanisms that allocate resources using approximation algorithms. Some approximation algorithms guarantee nearly 100% of the optimal welfare in the allocation problem but guarantee nothing when accounting for investment incentives. An algorithm's allocative and investment guarantees coincide if and only if its confirming negative externalities are sufficiently small. We introduce fast approximation algorithms for the knapsack problem that have no confirming negative externalities and guarantees close to 100% for both allocation and investment. [ABSTRACT FROM AUTHOR]

The identifying code problem for a given graph involves finding a minimum subset of vertices such that each vertex of the graph is uniquely specified by its nonempty neighborhood within the identifying code. The combinatorial optimization problem has a wide variety of applications in location and detection schemes. Finding an identifying code of minimum possible size is a difficult task. In fact, it has been proven to be computationally intractable (NP-complete). Therefore, the use of heuristics to provide good approximations in a reasonable amount of time is justified. In this work, we present a new population-based local search algorithm for finding identifying codes of minimum cost. Computational experiments show that the proposed approach was found to be more effective than other state-of-the-art algorithms at generating high-quality solutions in different types of graphs with varying numbers of vertices. [ABSTRACT FROM AUTHOR]

In this research, we investigate Hilfer-type FDDEs of both linear and nonlinear nature, with orders α and β. We studied some Riemann-Liouville, Caputo-Liouville, and Hilfer fractional derivatives properties; and then used them to convert our fractional delay problem into an equivalent fractional Volterra delay problem. After that, for the resulting fractional Volterra delay problem, using the CMT, existence-uniqueness is demonstrated. For numerical solutions, we studied the orthogonal shifted Legendre polynomials and used them as the basis for the Galerkin algorithm to find an approximation solution to the corresponding FDDE. By employing this algorithm, the provided FDDE is converted into a series of algebraic systems. By solving this system, the approximated solutions for the equation are obtained. The main algorithm advantage is that the number of needed iterations is low compared with the soft gained results. Some linear and nonlinear numerical applications together with several figures and tables are utilized to prove the performance and accuracy of the algorithm. The outcomes results are considered according to the given analysis and the numerical method was offered in the last section with several hints to guide future work. [ABSTRACT FROM AUTHOR]

The problem of deletion of vertices to a hereditary graph class is a well-studied problem in parameterized complexity. Recently, a natural extension of the problem was initiated where we are given a finite set of hereditary graph classes and we determine whether k vertices can be deleted from a given graph so that the connected components of the resulting graph belong to one of the given hereditary graph classes. The problem is shown to be fixed parameter tractable (FPT) when the deletion problem to each of the given hereditary graph classes is fixed-parameter tractable, and the property of being in any of the graph classes is expressible in the counting monodic second order (CMSO) logic. This paper focuses on pairs of specific graph classes (Π 1 , Π 2) in which we would like the connected components of the resulting graph to belong to, and design simpler and more efficient FPT algorithms. [ABSTRACT FROM AUTHOR]

Voronoi diagrams on triangulated surfaces based on the geodesic metric play a key role in many applications of computer graphics. Previous methods of constructing such Voronoi diagrams generally depended on having an exact geodesic metric. However, exact geodesic computation is time-consuming and has high memory usage, limiting wider application of geodesic Voronoi diagrams (GVDs). In order to overcome this issue, instead of using exact methods, we reformulate a graph method based on Steiner point insertion, as an effective way to obtain geodesic distances. Further, since a bisector comprises hyperbolic and line segments, we utilize Apollonius diagrams to encode complicated structures, enabling Voronoi diagrams to encode a medial-axis surface for a dense set of boundary samples. Based on these strategies, we present an approximation algorithm for efficient Voronoi diagram construction on triangulated surfaces. We also suggest a measure for evaluating similarity of our results to the exact GVD. Although our GVD results are constructed using approximate geodesic distances, we can get GVD results similar to exact results by inserting Steiner points on triangle edges. Experimental results on many 3D models indicate the improved speed and memory requirements compared to previous leading methods. [ABSTRACT FROM AUTHOR]

Recently, complicated spatial search algorithms have emerged as spatial-information-based applications, such as location-based services (LBS), and have become very diverse and frequent. The aggregate nearest neighbor (ANN) search is an extension of the existing nearest neighbor (NN) search; it finds the object p * that minimizes G { d (p * , q i) , q i ∈ Q } from a set Q of M (≥1) query objects, where G is an aggregate function and d () is the distance between two objects. The flexible aggregate nearest neighbor (FANN) search is an extension of the ANN search by introducing flexibility factor  ϕ (0 < ϕ ≤ 1) ; it finds the object p * that minimizes G { d (p * , q i) , q i ∈ Q ϕ } from Q ϕ , a subset of Q with | Q ϕ | = ϕ | Q | . This paper proposes an efficient ϵ -approximate k-FANN (k ≥ 1) search algorithm for an arbitrary approximation ratio ϵ (≥1) in road networks. In general, ϵ -approximate algorithms are expected to give an improved search performance at the cost of allowing an error ratio of up to the given ϵ. Since the optimal value of ϵ varies greatly depending on applications and cases, the approximate algorithm for an arbitrary ϵ is essential. We prove that the error ratios of the approximate FANN objects returned by our algorithm do not exceed the given ϵ. To the best of our knowledge, our algorithm is the first ϵ -approximate k-FANN search algorithm in road networks for an arbitrary ϵ. Through a series of experiments using various real-world road network datasets, we demonstrated that our approximate algorithm always outperformed the previous state-of-the-art exact algorithm and that the error ratios of the approximate FANN objects were significantly lower than the given ϵ value. [ABSTRACT FROM AUTHOR]

The edit distance between two strings is defined as the smallest number of insertions, deletions, and substitutions that need to be made to transform one of the strings to another one. Approximating edit distance in subquadratic time is "one of the biggest unsolved problems in the field of combinatorial pattern matching" [37]. Our main result is a quantum constant approximation algorithm for computing the edit distance in truly subquadratic time. More precisely, we give an O(n1.810) quantum algorithm that approximates the edit distance within a factor of 3. We further extend this result to an O(n1.708) quantum algorithm that approximates the edit distance within a larger constant factor. Our solutions are based on a framework for approximating edit distance in parallel settings. This framework requires as black box an algorithm that computes the distances of several smaller strings all at once. For a quantum algorithm, we reduce the black box to metric estimation and provide efficient algorithms for approximating it.We further show that this framework enables us to approximate edit distance in distributed settings. To this end, we provide a MapReduce algorithm to approximate edit distance within a factor of 1+∈, with sublinearly many machines and sublinear memory. Also, our algorithm runs in a logarithmic number of rounds. [ABSTRACT FROM AUTHOR]

A (unit) disk graph is the intersection graph of closed (unit) disks in the plane. Almost three decades ago, an elegant polynomial-time algorithm was found for Maximum Cliqe on unit disk graphs [Clark, Colbourn, Johnson; Discrete Mathematics '90]. Since then, it has been an intriguing open question whether or not tractability can be extended to general disk graphs. We show that the disjoint union of two odd cycles is never the complement of a disk graph nor of a unit (3-dimensional) ball graph. From that fact and existing results, we derive a simple QPTAS and a subexponential algorithm running in time 2õ (n²/3 ) for Maximum Cliqe on disk and unit ball graphs. We then obtain a randomized EPTAS for computing the independence number on graphs having no disjoint union of two odd cycles as an induced subgraph, bounded VC-dimension, and linear independence number. This, in combination with our structural results, yields a randomized EPTAS for Max Cliqe on disk and unit ball graphs. Max Cliqe on unit ball graphs is equivalent to finding, given a collection of points in R³, a maximum subset of pointswith diameter at most some fixed value. In stark contrast, Maximum Cliqe on ball graphs and unit 4-dimensional ball graphs, as well as intersection graphs of filled ellipses (even close to unit disks) or filled triangles is unlikely to have such algorithms. Indeed, we showthat, for all those problems, there is a constant ratio of approximation that cannot be attained even in time 2n1-ε, unless the Exponential Time Hypothesis fails. [ABSTRACT FROM AUTHOR]

In this article, we study the geometry of units and ideals of cyclotomic rings and derive an algorithm to find a mildly short vector in any given cyclotomic ideal lattice in quantum polynomial time, under some plausible number-theoretic assumptions. More precisely, given an ideal lattice of the cyclotomic ring of conductor m, the algorithm finds an approximation of the shortest vector by a factor exp(-õ (vm)). This result exposes an unexpected hardness gap between these structured lattices and general lattices: The best known polynomial time generic lattice algorithms can only reach an approximation factor exp(-O (m)). Following a recent series of attacks, these results call into question the hardness of various problems over structured lattices, suchas Ideal-SVP and Ring-LWE, upon which relies the security of a number of cryptographic schemes. [ABSTRACT FROM AUTHOR]

Fuzzy rough set theory has been successfully applied to many attribute reduction methods, in which the lower approximation set plays a pivotal role. However, the definition of lower approximation used has ignored the information conveyed by the upper approximation and the boundary region. This oversight has resulted in an unreasonable relation representation of the target set. Despite the fact that scholars have proposed numerous enhancements to rough set models, such as the variable precision model, none have successfully resolved the issues inherent in the classical models. To address this limitation, this paper proposes an unsupervised attribute reduction algorithm for mixed data based on an improved optimal approximation set. Firstly, the theory of an improved optimal approximation set and its associated algorithm are proposed. Subsequently, we extend the classical theory of optimal approximation sets to fuzzy rough set theory, leading to the development of a fuzzy improved approximation set method. Finally, building on the proposed theory, we introduce a novel, fuzzy optimal approximation-set-based unsupervised attribute reduction algorithm (FOUAR). Comparative experiments conducted with all the proposed algorithms indicate the efficacy of FOUAR in selecting fewer attributes while maintaining and improving the performance of the machine learning algorithm. Furthermore, they highlight the advantage of the improved optimal approximation set algorithm, which offers higher similarity to the target set and provides a more concise expression. [ABSTRACT FROM AUTHOR]

The article presents the development of new physics-informed evolutionary neural network learning algorithms. These algorithms aim to address the challenges of ill-posed problems by constructing a population close to the Pareto front. The study focuses on comparing the algorithm's capabilities based on three quality criteria of solutions. To evaluate the algorithms' performance, two benchmark problems have been used. The first involved solving the Laplace equation in square regions with discontinuous boundary conditions. The second problem considered the absence of boundary conditions but with the presence of measurements. Additionally, the study investigates the influence of hyperparameters on the final results. Comparisons have been made between the proposed algorithms and standard algorithms for constructing neural networks based on physics (commonly referred to as vanilla's algorithms). The results demonstrate the advantage of the proposed algorithms in achieving better performance when solving incorrectly posed problems. Furthermore, the proposed algorithms have the ability to identify specific solutions with the desired smoothness. [ABSTRACT FROM AUTHOR]

Ride-pooling, which accommodates multiple passenger requests in a single trip, has the potential to substantially enhance the throughput of mobility-on-demand (MoD) systems. This paper investigates MoD systems that operate mixed fleets composed of "basic supply" and "augmented supply" vehicles. When the basic supply is insufficient to satisfy demand, augmented supply vehicles can be repositioned to serve rides at a higher operational cost. We formulate the joint vehicle repositioning and ride-pooling assignment problem as a two-stage stochastic integer program, where repositioning augmented supply vehicles precedes the realization of ride requests. Sequential ride-pooling assignments aim to maximize total utility or profit on a shareability graph: a hypergraph representing the matching compatibility between available vehicles and pending requests. Two approximation algorithms for midcapacity and high-capacity vehicles are proposed in this paper; the respective approximation ratios are 1 / p 2 and (e − 1) / (2 e + o (1)) p ln p , where p is the maximum vehicle capacity plus one. Our study evaluates the performance of these approximation algorithms using an MoD simulator, demonstrating that these algorithms can parallelize computations and achieve solutions with small optimality gaps (typically within 1%). These efficient algorithms pave the way for various multimodal and multiclass MoD applications. History: This paper has been accepted for the Transportation Science Special Issue on Emerging Topics in Transportation Science and Logistics. Funding: This work was supported by the National Science Foundation [Grants CCF-2006778 and FW-HTF-P 2222806], the Ford Motor Company, and the Division of Civil, Mechanical, and Manufacturing Innovation [Grants CMMI-1854684, CMMI-1904575, and CMMI-1940766]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2021.0349. [ABSTRACT FROM AUTHOR]

In multi-access edge computing (MEC) networks, parallelized service function chains (P-SFCs) can provide low-delay network services for mobile users by deploying virtualized network functions (VNFs) to process user requests in parallel. These VNFs are unreliable due to software faults and server failures. A practical way to address this is to deploy idle backup VNFs (BVNFs) near these active VNFs and activate them when active VNFs fail. However, deploying BVNFs preempts server resources and decreases the number of accepted user requests. Thus, this paper proposes a reliability enhancement approach that uses BVNFs satisfying the delay requirement as active VNFs to form P-SFCs, which contributes to the delay reduction and reliability enhancement. Since the resource capacities of edge servers can only deploy a certain number of P-SFCs and BVNFs, establishing how to deploy the minimum number of P-SFCs and BVNFs to satisfy the delay and reliability requirements of mobile users and maximize the number of accepted user requests is a challenging problem. In this paper, we first model the dynamics of delay and reliability caused by VNF parallelization and BVNFs deployment, then formulate the joint deployment problem of P-SFCs and BVNFs. Next, we design an approximation algorithm to deploy critical VNFs and BVNFs on a target edge server and schedule the data traffic of user requests processed by P-SFCs. Experimental results based on real-world datasets show that our proposed algorithm outperforms two benchmark algorithms in terms of throughput, delay, reliability, and resource utilization. [ABSTRACT FROM AUTHOR]

The Internet of Things (IoT) has become increasingly popular, and its communication requirements have grown beyond what traditional ground networks can handle. The space–air–ground (SAG) integrated network has been proposed as a potential solution, where unmanned aerial vehicles (UAVs) collect data from IoT devices and transmit them to satellites. However, the limited energy of UAVs is one of the key factors restricting communication performance, so it is necessary to consider communication energy efficiency (EE). In addition, the improvement of EE will bring about the decline of spectral efficiency (SE). Therefore we consider the tradeoff between EE and SE. Considering a SAG-IoT network, the focus of the paper is to optimize sub-channel selection, power control, and UAV position deployment to maximize EE and SE of the network, which is a multi-objective optimization (MOO) problem. On this premise, we try to improve the data throughput between IoT devices and UAVs. To solve this MOO problem, we use the ϵ -constraint to convert it into a single-objective optimization problem. We then employ various optimization algorithms such as the Dinkelbach algorithm, successive convex approximation algorithm, Lagrange dual algorithm, and block coordinate descent algorithm to solve the mixed integer non-convex problem. Simulation results show that the proposed algorithm converges to at least one sub-optimal solution. [ABSTRACT FROM AUTHOR]

In this paper, we present self-adaptive inertial iterative algorithms involving Yosida approximation to investigate a split variational inclusion problem (SVIP) and common solutions of a fixed point problem (FPP) and SVIP in Hilbert spaces. We analyze the weak convergence of the proposed iterative algorithm to explore the approximate solution of the SVIP and strong convergence to estimate the common solution of the SVIP and FPP under some mild suppositions. A numerical example is demonstrated to validate the theoretical findings, and comparison of our iterative methods with some known schemes is outlined. [ABSTRACT FROM AUTHOR]

For point sets A, B ⊂ Rd, |A| = |B| = n, and for a parameter ε > 0, we present a Monte Carlo algorithm that computes, in O(npoly(logn, 1/ε)) time, an ε-approximate perfect matching of A and B under any Lp-norm with high probability; the previously best-known algorithm takes Ω(n3/2) time. We approximate the Lp-norm using a distance function, d(·, ·) based on a randomly shifted quad-tree. The algorithm iteratively generates an approximate minimum-cost augmenting path under d(·, ·) in time proportional, within a polylogarithmic factor, to the length of the path. We show that the total length of the augmenting paths generated by the algorithm is O((n/ε) logn), implying that the running time of our algorithm is O(npoly(logn, 1/ε)). [ABSTRACT FROM AUTHOR]

We introduce and study two natural generalizations of the Connected Vertex Cover (VC) problem: the p -Edge-Connected and p -Vertex-Connected VC problem (where p ≥ 2 is a fixed integer). We obtain an 2 O (p k) n O (1) -time algorithm for p -Edge-Connected VC and an 2 O (k 2) n O (1) -time algorithm for p -Vertex-Connected VC. Thus, like Connected VC, both constrained VC problems are FPT. Furthermore, like Connected VC, neither problem admits a polynomial kernel unless NP ⊆ coNP/poly, which is highly unlikely. We prove however that both problems admit time efficient polynomial sized approximate kernelization schemes. Finally, we describe a 2 (p + 1) -approximation algorithm for the p -Edge-Connected VC. The proofs for the new VC problems require more sophisticated arguments than for Connected VC. In particular, for the approximation algorithm we use Gomory-Hu trees and for the approximate kernels a result on small-size spanning p -vertex/edge-connected subgraphs of a p -vertex/edge-connected graph by Nishizeki and Poljak (1994) [30] and Nagamochi and Ibaraki (1992) [27]. [ABSTRACT FROM AUTHOR]

Featured Application: This article assesses different text representations for labeling unmarked dialog data, which can be applied to identify user intents directly relevant to dialog systems. Chatbots are becoming increasingly popular and require the ability to interpret natural language to provide clear communication with humans. To achieve this, intent detection is crucial. However, current applications typically need a significant amount of annotated data, which is time-consuming and expensive to acquire. This article assesses the effectiveness of different text representations for annotating unlabeled dialog data through a pipeline that examines both classical approaches and pre-trained transformer models for word embedding. The resulting embeddings were then used to create sentence embeddings through pooling, followed by dimensionality reduction, before being fed into a clustering algorithm to determine the user's intents. Therefore, various pooling, dimension reduction, and clustering algorithms were evaluated to determine the most appropriate approach. The evaluation dataset contains a variety of user intents across different domains, with varying intent taxonomies within the same domain. Results demonstrate that transformer-based models perform better text representation than classical approaches. However, combining several clustering algorithms and embeddings from dissimilar origins through ensemble clustering considerably improves the final clustering solution. Additionally, applying the uniform manifold approximation and projection algorithm for dimension reduction can substantially improve performance (up to 20%) while using a much smaller representation. [ABSTRACT FROM AUTHOR]

For maneuvering target tracking, the interactive multiple model (IMM) algorithm and its variants have shown good performance, among which the variable structure IMM (VSIMM) algorithm is the most widely studied one. The approximation degree of the algorithm and the matching degree of the model subset will affect the performance of the VSIMM. In addition, considering that smoothing can provide better estimation of the target state, a new adaptive VSIMM filtering and smoothing (AVSIMMFS) algorithm is proposed in this paper. First, an accurate model of the VSIMM algorithm is established, in which the IMM is run in parallel with and independently from the different model subsets, and the state estimation of the model subset with the highest probability is selected as the final estimation result. Then, an adaptive VSIMM (AVSIMM) algorithm was designed based on the VSIMM algorithm. The adaptation is reflected in the construction of a new model subset from the original model subsets, which improves the matching degree between the model subset and the actual maneuvering model of the target. Finally, by smoothing the filtering data of the AVSIMM algorithm, the AVSIMMFS algorithm is obtained. Because of the combination of forward filtering and backward smoothing, the target tracking accuracy is further improved. Simulation results show that the tracking performance of the AVSIMMFS algorithm is better than that of other methods. [ABSTRACT FROM AUTHOR]

We consider a variant of the k-center clustering problem in I R d , where the centers can be divided into two subsets—one, the red centers of size p, and the other, the blue centers of size q, such that p + q = k , and each red center and each blue center must be a distance of at least some given α ≥ 0 apart. The aim is to minimize the covering radius. We provide a bi-criteria approximation algorithm for the problem and a polynomial time algorithm for the constrained problem where all centers must lie on a given line ℓ. Additionally, we present a polynomial time algorithm for the case where only the orientation of the line is fixed in the plane ( d = 2 ), although the algorithm works even in I R d by constraining the line to lie in a plane and with a fixed orientation. [ABSTRACT FROM AUTHOR]

We present SimultaneousGreedys, a deterministic algorithm for constrained submodular maximization. At a high level, the algorithm maintains l solutions and greedily updates them in a simultaneous fashion. SIMULTANEOUSGREEDYS achieves the tightest known approximation guarantees for both k-extendible systems and the more general k-systems, which are (k+1)²/k = k+O(1) and (1+√k+2)² = k+O(√k), respectively. We also improve the analysis of REPEATEDGREEDY, showing that it achieves an approximation ratio of k+O(√k) for k-systems when allowed to run for O(√k) iterations, an improvement in both the runtime and approximation over previous analyses. We demonstrate that both algorithms may be modified to run in nearly linear time with an arbitrarily small loss in the approximation. Both SIMULTANEOUSGREEDYS and REPEATEDGREEDY are flexible enough to incor porate the intersection of m additional knapsack constraints, while retaining similar approximation guarantees: both algorithms yield an approximation guarantee of roughly k+2m + O(√k+m) for k-systems and SIMULTANEOUSGREEDYS enjoys an improved approximation guarantee of k+2m + O(√m) for k-extendible systems. To complement our algorithmic contributions, we prove that no algorithm making polynomially many oracle queries can achieve an approximation better than k + 1/2 - ε. We also present SubmodularGreedy.jl, a Julia package which implements these algorithms. Finally, we test these algorithms on real datasets. [ABSTRACT FROM AUTHOR]

Hierarchical clustering is a data analysis method that has been used for decades. Despite its widespread use, the method has an underdeveloped analytical foundation. Having a well understood foundation would both support the currently used methods and help guide future improvements. The goal of this paper is to give an analytic framework to better understand observations seen in practice. This paper considers the dual of a problem framework for hierarchical clustering introduced by Dasgupta (2016). The main result is that one of the most popular algorithms used in practice, average linkage agglomerative clustering, has a small constant approximation ratio for this objective. To contrast, this paper establishes that using several other popular algorithms, including bisecting k-means divisive clustering, have a very poor lower bound on its approximation ratio for the same objective. However, we show that there are divisive algorithms that perform well with respect to this objective by giving two constant approximation algorithms. This paper is some of the first work to establish guarantees on widely used hierarchical algorithms for a natural objective function. This objective and analysis give insight into what these popular algorithms are optimizing and when they will perform well. [ABSTRACT FROM AUTHOR]

Adversarial attacks have been extensively studied in recent years since they can identify the vulnerability of deep learning models before deployed. In this paper, we consider the black-box adversarial setting, where the adversary needs to craft adversarial examples without access to the gradients of a target model. Previous methods attempted to approximate the true gradient either by using the transfer gradient of a surrogate white-box model or based on the feedback of model queries. However, the existing methods inevitably suffer from low attack success rates or poor query efficiency since it is difficult to estimate the gradient in a high-dimensional input space with limited information. To address these problems and improve black-box attacks, we propose two prior-guided random gradient-free (PRGF) algorithms based on biased sampling and gradient averaging, respectively. Our methods can take the advantage of a transfer-based prior given by the gradient of a surrogate model and the query information simultaneously. Through theoretical analyses, the transfer-based prior is appropriately integrated with model queries by an optimal coefficient in each method. Extensive experiments demonstrate that, in comparison with the alternative state-of-the-arts, both of our methods require much fewer queries to attack black-box models with higher success rates. [ABSTRACT FROM AUTHOR]

Multiobjective optimization approaches have allowed the improvement of technical features in industrial processes, focusing on more accurate approaches for solving complex engineering problems and support decision-making. This paper proposes a hybrid approach to optimize the 3D printing technology parameters, integrating the design of experiments and multiobjective optimization methods, as an alternative to classical parametrization design used in machining processes. Alongside the approach, a multiobjective differential evolution with uniform spherical pruning (usp-MODE) algorithm is proposed to serve as an optimization tool. The parametrization design problem considered in this research has the following three objectives: to minimize both surface roughness and dimensional accuracy while maximizing the mechanical resistance of the prototype. A benchmark with non-dominated sorting genetic algorithm II (NSGA-II) and with the classical sp-MODE is used to evaluate the performance of the proposed algorithm. With the increasing complexity of engineering problems and advances in 3D printing technology, this study demonstrates the applicability of the proposed hybrid approach, finding optimal combinations for the machining process among conflicting objectives regardless of the number of decision variables and goals involved. To measure the performance and to compare the results of metaheuristics used in this study, three Pareto comparison metrics have been utilized to evaluate both the convergence and diversity of the obtained Pareto approximations for each algorithm: hyper-volume (H), g-Indicator (G), and inverted generational distance. To all of them, ups-MODE outperformed, with significant figures, the results reached by NSGA-II and sp-MODE algorithms. [ABSTRACT FROM AUTHOR]

Owing to its good compression ability, discrete cosine transform (DCT) is widely used in signal processing, including high-efficiency video coding (HEVC). For efficient implementation, approximate DCTs and integer DCTs were proposed, but the challenge in the tradeoff between coding performance and implementation cost always exists. To solve this problem, this article proposes a new algorithm to derive Int-DCT with good coding performance and low hardware cost. To address the multiobjective optimization problem, we extract information from the initially shortlisted transform matrices to derive the weighting factors for the different matrices properties. Those properties having a higher impact to the performance are assigned with higher weights and vice versa. Subsequently, an efficient search algorithm is proposed to shortlist those candidates which can lead to better coding performance evaluated by the proposed measure. Last but not the least, a splitting method is proposed to search the efficient extended double-base number system (EDBNS) representation of the coefficients for hardware implementation and select the solution which encounters the lowest cost. The experimental results in ASIC demonstrate that the implementation area and power cost of designs by the new algorithm are reduced by at least 11.1% and 17.5% for 32-point transform, respectively, over other competing algorithms. Meanwhile, the transforms generated by the proposed algorithm causes negligible impact to coding performance compared to the original transforms in HEVC. [ABSTRACT FROM AUTHOR]

We study two generalizations of classic clustering problems called dynamic ordered k-median and dynamic k-supplier , where the points that need clustering evolve over time, and we are allowed to move the cluster centers between consecutive time steps. In these dynamic clustering problems, the general goal is to minimize certain combinations of the service cost of points and the movement cost of centers, or to minimize one subject to some constraints on the other. We obtain a constant-factor approximation algorithm for dynamic ordered k -median under mild assumptions on the input. We give a 3-approximation for dynamic k -supplier and a multi-criteria approximation for its outlier version where some points can be discarded, when the number of time steps is two. We complement the algorithms with almost matching hardness results. [ABSTRACT FROM AUTHOR]

We present prior robust algorithms for a large class of resource allocation problems where requests arrive one-by-one (online), drawn independently from an unknown distribution at every step. We design a single algorithm that, for every possible underlying distribution, obtains a 1−∊ fraction of the profit obtained by an algorithm that knows the entire request sequence ahead of time. The factor ∊ approaches 0 when no single request consumes/contributes a significant fraction of the global consumption/contribution by all requests together. We show that the tradeoff we obtain here that determines how fast ∊ approaches 0, is near optimal: We give a nearly matching lower bound showing that the tradeoff cannot be improved much beyond what we obtain. Going beyond the model of a static underlying distribution, we introduce the adversarial stochastic input model, where an adversary, possibly in an adaptive manner, controls the distributions from which the requests are drawn at each step. Placing no restriction on the adversary, we design an algorithm that obtains a 1−∊ fraction of the optimal profit obtainable w.r.t. the worst distribution in the adversarial sequence. Further, if the algorithm is given one number per distribution, namely the optimal profit possible for each of the adversary's distribution, then we design an algorithm that achieves a 1−∊ fraction of the weighted average of the optimal profit of each distribution the adversary picks. In the offline setting we give a fast algorithm to solve very large linear programs (LPs) with both packing and covering constraints. We give algorithms to approximately solve (within a factor of 1+∊) the mixed packing-covering problem with O(γ m log (n/Δ)/∊2) oracle calls where the constraint matrix of this LP has dimension n× m, the success probability of the algorithm is 1−Δ, and γ quantifies how significant a single request is when compared to the sum total of all requests. We discuss implications of our results to several special cases including online combinatorial auctions, network routing, and the adwords problem. [ABSTRACT FROM AUTHOR]

Many inverse problems in machine learning, system identification, and image processing include nuisance parameters, which are important for the recovering of other parameters. Separable nonlinear optimization problems fall into this category. The special separable structure in these problems has inspired several efficient optimization strategies. A well-known method is the variable projection (VP) that projects out a subset of the estimated parameters, resulting in a reduced problem that includes fewer parameters. The expectation maximization (EM) is another separated method that provides a powerful framework for the estimation of nuisance parameters. The relationships between EM and VP were ignored in previous studies, though they deal with a part of parameters in a similar way. In this article, we explore the internal relationships and differences between VP and EM. Unlike the algorithms that separate the parameters directly, the hierarchical identification algorithm decomposes a complex model into several linked submodels and identifies the corresponding parameters. Therefore, this article also studies the difference and connection between the hierarchical algorithm and the parameter-separated algorithms like VP and EM. In the numerical simulation part, Monte Carlo experiments are performed to further compare the performance of different algorithms. The results show that the VP algorithm usually converges faster than the other two algorithms and is more robust to the initial point of the parameters. [ABSTRACT FROM AUTHOR]

Problem definition: We focus on modeling and evaluating an emergency service system in which cross-trained fire-medics are pooled and respond to both fire calls and medical emergencies. Academic/practical relevance: Fire demand in the United States has decreased dramatically in the last nearly four decades, whereas emergency medical calls have surged. With this changing landscape, cities are under pressure to reduce their budgets by closing fire stations. We evaluate the alternative of implementing a fire-medic system in terms of cost savings and response time performance. Methodology: A cross-trained fire-medic unit may be in one of three states: available, busy at an emergency medical incident, or busy at a fire call. An exact model for the fire-medic system has exponential complexity. We develop a fast approximation algorithm that has linear complexity and can be used to solve three-state problems of any size. Results: Our approximation algorithm yields accurate predictions of response times and unit workloads and provides rapid solution times. We apply our model to the fire-medic system in St. Paul, MN, and find close agreement between predicted and actual average response times. A traditional system would require 33% more personnel to achieve about the same average response times. In sensitivity analyses, we show that the fire-medic system outperforms a traditional system over a wide range of values for call rates and number of joint units. Managerial implications: The fire-medic system in St. Paul, MN, saves more than three million dollars annually. The greatest benefit of the fire-medic system is in reducing response times to medical emergencies. We also show that in a fire-medic system that includes separate engine units, it is advantageous to convert the separate engines to fire-medic units. Our fast approximation algorithm can be applied even in the largest cities that implement fire-medic systems to improve resource deployment and reduce costs. Funding: This work was supported by the Shanghai Science and Technology Development Foundation [Grant 21YF1420200]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/msom.2022.1140. [ABSTRACT FROM AUTHOR]

We study the problem of maximizing a nonmonotone submodular function subject to a cardinality constraint in the streaming model. Our main contribution is a single-pass (semi) streaming algorithm that uses roughly O (k / ε 2) memory, where k is the size constraint. At the end of the stream, our algorithm postprocesses its data structure using any off-line algorithm for submodular maximization and obtains a solution whose approximation guarantee is α / (1 + α) − ε , where α is the approximation of the off-line algorithm. If we use an exact (exponential time) postprocessing algorithm, this leads to 1 / 2 − ε approximation (which is nearly optimal). If we postprocess with the state-of-the-art offline approximation algorithm, whose guarantee is α = 0.385 , we obtain a 0.2779-approximation in polynomial time, improving over the previously best polynomial-time approximation of 0.1715. It is also worth mentioning that our algorithm is combinatorial and deterministic, which is rare for an algorithm for nonmonotone submodular maximization, and enjoys a fast update time of O ( ε −2 (log k + log (1 + α))) per element. [ABSTRACT FROM AUTHOR]

The variational quantum algorithm (VQA) is a hybrid classical–quantum algorithm. It can actually run in an intermediate-scale quantum device where the number of available qubits is too limited to perform quantum error correction, so it is one of the most promising quantum algorithms in the noisy intermediate-scale quantum era. In this paper, two ideas for solving the learning with errors problem (LWE) using VQA are proposed. First, after reducing the LWE problem into the bounded distance decoding problem, the quantum approximation optimization algorithm (QAOA) is introduced to improve classical methods. Second, after the LWE problem is reduced into the unique shortest vector problem, the variational quantum eigensolver (VQE) is used to solve it, and the number of qubits required is calculated in detail. Small-scale experiments are carried out for the two LWE variational quantum algorithms, and the experiments show that VQA improves the quality of the classical solutions. [ABSTRACT FROM AUTHOR]

Subgraph queries are routinely used to search for entities in richly attributed graphs e.g., social networks and knowledge graphs. With little knowledge of underlying data, users often need to rewrite queries multiple times to reach desirable answers. Why-questions are studied to clarify missing or unexpected query results. This paper makes a first step to answer Why-questions for entity search in attributed graphs. We consider three common types of Why-questions: Why-not, Why, and Why-rank, which suggest query manipulations that are responsible for user-specified missing, unexpected, and undesirably ranked entities, respectively. (1) We approach a general query rewriting paradigm that suggests to identify desired entities that are specified by Why-questions. We introduce measures that characterize good query rewrites by incorporating both query editing cost and answer closeness. (2) While computing optimal query rewrites is intractable, we develop feasible algorithms, from approximation to fast heuristics, and provide query rewrites with (near) optimality guarantees whenever possible, for Why, Why-not and Why-rank questions. We further show that our results remain intact for Why questions that (1) request a single query rewrite to clarify multiple types of entities, and (2) variants such as Why-empty and Why-so-many, by providing the matching algorithms. Using real-world graphs, we experimentally verify that our algorithms are effective and feasible for large graphs. Our case study also verifies their application in e.g., knowledge exploration. [ABSTRACT FROM AUTHOR]

Data deduplication saves storage space by identifying and removing repeats in the data stream. Compared with traditional compression methods, data deduplication schemes are more computationally efficient and are thus widely used in large scale storage systems. In this paper, we provide an information-theoretic analysis of the performance of deduplication algorithms on data streams in which repeats are not exact. We introduce a source model in which probabilistic substitutions are considered. More precisely, each symbol in a repeated string is substituted with a given edit probability. Deduplication algorithms in both the fixed-length scheme and the variable-length scheme are studied. The fixed-length deduplication algorithm is shown to be unsuitable for the proposed source model as it does not take into account the edit probability. Two modifications are proposed and shown to have performances within a constant factor of optimal for a specific class of source models with the knowledge of model parameters. We also study the conventional variable-length deduplication algorithm and show that as source entropy becomes smaller, the size of the compressed string vanishes relative to the length of the uncompressed string, leading to high compression ratios. [ABSTRACT FROM AUTHOR]

This article investigates the finite-time distributed approximate optimization problem of higher order multiagent systems, where the local cost functions are considered to be quadratic functions. This problem is solved via penalty-function-based method. First, by the penalty-function method, a global approximate cost function is constructed. Second, nonlinear distributed optimization algorithms are proposed for higher order multiagent systems by the tool of adding a power integrator technique. In the optimization algorithms design, the gradients of the approximate cost function are utilized. Under the proposed optimization algorithms, the agents approach the approximate optimal solution in finite time. Although there exist errors (they may be called approximation errors) between the approximate minimizers and the global accurate minimizer, the approximation errors can be regulated by penalty parameter and the relationship between the bound of the approximation errors and the penalty parameter is given explicitly. Furthermore, the proposed distributed approximate optimization algorithms are applied to the optimal rendezvous problem of wheeled multimobile robots, making the mobile robots achieve approximate optimization rendezvous in finite time. The effectiveness of the proposed distributed optimization algorithms and their applications to optimal rendezvous problem are validated by simulations. [ABSTRACT FROM AUTHOR]

We present two new algorithms for convex Mixed Integer Nonlinear Programming (MINLP), both based on the well known Extended Cutting Plane (ECP) algorithm proposed by Weterlund and Petersson. Our first algorithm, Refined Extended Cutting Plane (RECP), incorporates additional cuts to the MILP relaxation of the original problem, obtained by solving linear relaxations of NLP problems considered in the Outer Approximation algorithm. Our second algorithm, Linear Programming based Branch-and-Bound (LP-BB), applies the strategy of generating cuts that is used in RECP, to the linear approximation scheme used by the LP/NLP based Branch-and-Bound algorithm. Our computational results show that RECP and LP-BB are highly competitive with the most popular MINLP algorithms from the literature, while keeping the nice and desirable characteristic of ECP, of being a first-order method. [ABSTRACT FROM AUTHOR]

Sparse tensor best rank-1 approximation (BR1Approx), which is a sparsity generalization of the dense tensor BR1Approx, and is a higher-order extension of the sparse matrix BR1Approx, is one of the most important problems in sparse tensor decomposition and related problems arising from statistics and machine learning. By exploiting the multilinearity as well as the sparsity structure of the problem, four polynomial-time approximation algorithms are proposed, which are easily implemented, of low computational complexity, and can serve as initial procedures for iterative algorithms. In addition, theoretically guaranteed approximation lower bounds are derived for all the algorithms. We provide numerical experiments on synthetic and real data to illustrate the efficiency and effectiveness of the proposed algorithms; in particular, serving as initialization procedures, the approximation algorithms can help in improving the solution quality of iterative algorithms while reducing the computational time. [ABSTRACT FROM AUTHOR]

For several decades, much effort has been put into identifying classes of CNF formulas whose satisfiability can be decided in polynomial time. Classic results are the linear-time tractability of Horn formulas (Aspvall, Plass, and Tarjan, 1979) and Krom (i.e., 2CNF) formulas (Dowling and Gallier, 1984). Backdoors, introduced by Williams, Gomes and Selman (2003), gradually extend such a tractable class to all formulas of bounded distance to the class. Backdoor size provides a natural but rather crude distance measure between a formula and a tractable class. Backdoor depth, introduced by Mählmann, Siebertz, and Vigny (2021), is a more refined distance measure, which admits the utilization of different backdoor variables in parallel. We propose FPT approximation algorithms to compute backdoor depth into the classes Horn and Krom. This leads to a linear-time algorithm for deciding the satisfiability of formulas of bounded backdoor depth into these classes. [ABSTRACT FROM AUTHOR]