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A method for measuring the spectrum of admittance spectrum of piezoelectric elements in the pulsed excitation mode and its digital implementation are proposed. The method reduces the duration of measurements, and the processing algorithm increases the accuracy of the estimated parameters. To determine the characteristic frequencies, Q-factor, and parallel capacitance, an algorithm of fractional-rational approximation of the admittance spectrum in the resonant frequency range is used. [ABSTRACT FROM AUTHOR]

Policy gradient algorithms suffer from the large variance of gradient estimation. the algorithm of policy gradient with parameter based exploration mitigates this problem to some extent. However, PGPE estimates its gradient based on the Monte Carlo, which requires a large number of samples to achieve the fairly stable policy update. And thus hinders its application in the real world problem. In order to further reduce the variance of policy gradient, the algorithm of function approximation for policy gradients with parameter-based exploration (PGPE-FA) implements the algorithm of PGPE in the Actor-Critic framework. More specifically, the proposed method utilized value function to estimate the policy gradient, instead of using trajectory samples to estimate the policy gradient as PGPE method does, thereby reducing the variance of gradient estimation. Finally, the experiment verifies that the proposed algorithm can reduce the variance of gradient estimation. [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]

Modern applications of graph algorithms often involve the use of the output sets (usually, a subset of edges or vertices of the input graph) as inputs to other algorithms. Since the input graphs of interest are large and dynamic, it is desirable for an algorithm's output to not change drastically when a few random edges are removed from the input graph, so as to prevent issues in postprocessing. Alternately, having such a guarantee also means that one can revise the solution obtained by running the algorithm on the original graph in just a few places in order to obtain a solution for the new graph. We formalize this feature by introducing the notion of average sensitivity of graph algorithms, which is the average earth mover's distance between the output distributions of an algorithm on a graph and its subgraph obtained by removing an edge, where the average is over the edges removed and the distance between two outputs is the Hamming distance. In this work, we initiate a systematic study of average sensitivity of graph algorithms. After deriving basic properties of average sensitivity such as composition, we provide efficient approximation algorithms with low average sensitivities for concrete graph problems, including the minimum spanning forest problem, the global minimum cut problem, the minimum s-t cut problem, and the maximum matching problem. In addition, we prove that the average sensitivity of our global minimum cut algorithm is almost optimal, by showing a nearly matching lower bound. We also show that every algorithm for the 2-coloring problem has average sensitivity linear in the number of vertices. One of the main ideas involved in designing our algorithms with low average sensitivity is the following fact: if the presence of a vertex or an edge in the solution output by an algorithm can be decided locally, then the algorithm has a low average sensitivity, allowing us to reuse the analyses of known subline artime algorithms and local computation algorithms. Using this fact in conjunction with our average sensitivity lower bound for 2-coloring, we show that every local computation algorithm for 2-coloring has query complexity linear in the number of vertices, thereby answering an open question. [ABSTRACT FROM AUTHOR]

Motivated by an application in cancer genomics, Hajirasouliha and Raphael [Proceedings of the 14th International Workshop on Algorithms in Bioinformatics, 2014, pp. 354-367] proposed the split-row problem (SR). In this problem, an m\times n binary matrix M is given. A split-row operation on M is defined as replacing a row r by k > 1 rows r(1), r(2), . . ., r(k) whose bitwise OR is equal to r. The cost of the operation is the number of additional rows induced, that is, k 1. The goal is to find a sequence of split-row operations that transforms M into a matrix corresponding to a perfect phylogeny and the total cost is minimized. Recently, Hujdurovi\'c et al. [ACM Trans. Algorithms, 14 (2018), 26] proved the APX-hardness of SR and presented efficient exact and approximation algorithms. The parameterized study of SR was left as a direction for future work. Let\varepsilon (M) denote the minimum total cost. This paper gives an O*(2min(n,2x(M))-time exact algorithm for SR. This result indicates that SR is fixed-parameter tractable when parameterized by E (M). In addition, in the worst case, our algorithm requires O* (2n) time, significantly improving the previous upper bound of O\ast (nn). Hujdurovi\'c et al.'s exact algorithm can be modified to solve a variant of SR, called the distinct split-row problem (DSR). Our algorithm can be adapted to this variant as well. In addition, our algorithms can be extended to solve SR and DSR with the following additional constraint: only the rows in a given subset are allowed to be split. [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 introduce a new algorithm for estimating the lower bounds for the star discrepancy of any arbitrary point sets in [ 0 , 1 ] s . Computing the exact star discrepancy is known to be an NP-hard problem, so we have been looking for effective approximation algorithms. The star discrepancy can be thought of as the maximum of a function called the local discrepancy, and we will develop approximation algorithms to maximize this function. Our algorithm is analogous to the random walk algorithm described in one of our previous papers [M. Alsolami and M. Mascagni, A random walk algorithm to estimate a lower bound of the star discrepancy, Monte Carlo Methods Appl.28 (2022), 4, 341–348.]. We add a statistical technique to the random walk algorithm by implementing the Metropolis algorithm in random walks on each chosen dimension to accept or reject this movement. We call this Metropolis random walk algorithm. In comparison to all previously known techniques, our new algorithm is superior, especially in high dimensions. Also, it can quickly determine the precise value of the star discrepancy in most of our data sets of various sizes and dimensions, or at least the lower bounds of the star discrepancy. [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]

In this paper we estimate the expected error of a stochastic approximation algorithm where the maximum of a function is found using finite differences of a stochastic representation of that function. An error estimate of the order $n^{-1/5}$ for the n th iteration is achieved using suitable parameters. The novelty with respect to previous studies is that we allow the stochastic representation to be discontinuous and to consist of possibly dependent random variables (satisfying a mixing condition). [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]

In real-life scenarios, both the vertex weight and edge weight in a network are hard to define exactly. We can incorporate the fuzziness into a network to handle this type of uncertain situation. Here, we use triangular fuzzy number to describe the vertex weight and edge weight of a fuzzy network G. In this paper, we consider weighted k-domination problem in fuzzy network. The weighted k-domination (WKD) problem is to find a k dominating set D which minimizes the cost f (D) : = ∑u∈Dw (u) + ∑v∈V\D min {∑u∈Sw (uv) |S ⊆ N (v) ∩ D, |S| = k}. First, we put forward an integer linear programming model with a polynomial number of constrains for the WKD problem. If G is a cycle, we design a dynamic algorithm to determine its exact weighted 2-domination number. If G is a tree, we give a label algorithm to determine its exact weighted 2-domination number. Combining a primal-dual method and a greedy method, we put forward an approximation algorithm for general fuzzy network on the WKD problem. Finally, we describe an application of the WKD problem to police camp problem. [ABSTRACT FROM AUTHOR]

Many network design problems deal with the design of low-cost networks that are resilient to the failure of their elements (such as nodes or links). One such problem is Connectivity Augmentation, with the goal of cheaply increasing the (edge- or node-)connectivity of a given network from a value k to k + 1 . The problem is NP-hard for k ≥ 1 , and the most studied setting focuses on the case of edge-connectivity with k = 1 . In this work, we give a 1.892-approximation algorithm for the NP-hard problem of augmenting the node-connectivity of any given graph from 1 to 2, which improves upon the state-of-the-art approximation previously developed in the literature. The starting point of our work is a known reduction from Connectivity Augmentation to some specific instances of the Node-Steiner Tree problem, and our result is obtained by developing a new and simple analysis of the iterative randomized rounding technique when applied to such Steiner Tree instances. Our results also imply a 1.892-approximation algorithm for the problem of augmenting the edge-connectivity of a given graph from any value k to k + 1 . While this does not beat the best approximation factor known for this problem, a key point of our work is that the analysis of our approximation factor is less involved when compared to previous results in the literature. In addition, our work gives new insights on the iterative randomized rounding method, that might be of independent interest. [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 describe a polynomial-time algorithm which, given a graph G with treewidth t, approximates the path-width of G to within a ratio of O(t√log t). This is the first algorithm to achieve an f(t)-approximation for some function f. Our approach builds on the following key insight: every graph with large pathwidth has large treewidth or contains a subdivision of a large complete binary tree. Specifically, we show that every graph with pathwidth at least th + 2 has treewidth at least t or contains a subdivision of a complete binary tree of height h + 1. The bound th + 2 is best possible up to a multiplicative constant. This result was motivated by, and implies (with c = 2), the following conjecture of Kawarabayashi and Rossman (SODA'18): there exists a universal constant c such that every graph with pathwidth Ω(kc) has treewidth at least k or contains a subdivision of a complete binary tree of height k. Our main technical algorithm takes a graph G and some (not necessarily optimal) tree decomposition of G of width t' in the input, and it computes in polynomial time an integer h, a certificate that G has pathwidth at least h, and a path decomposition of G of width at most (t' + 1)h + 1. The certificate is closely related to (and implies) the existence of a subdivision of a complete binary tree of height h. The approximation algorithm for pathwidth is then obtained by combining this algorithm with the approximation algorithm of Feige, Hajiaghayi, and Lee (STOC'05) for treewidth. [ABSTRACT FROM AUTHOR]

Parameter servers (PSs) placement is one of the most important factors for global model training on distributed deep learning. This paper formulates a novel problem for placement strategy of PSs in the dynamic available storage capacity, with the objective of minimizing the training time of the distributed deep learning under the constraints of storage capacity and the number of local PSs. Then, we provide the proof for the NP-hardness of the proposed problem. The whole training epochs are divided into two parts, i.e. the first epoch and the other epochs. For the first epoch, an approximation algorithm and a rounding algorithm are proposed in this paper, to solve the proposed problem. For the other epochs, an adjustment algorithm is proposed, by continuously adjusting the decisions for placement strategy of PSs to decrease the training time of the global model. Simulation results show that the proposed approximation algorithm and rounding algorithm perform better than existing works for all cases, in terms of the training time of global model. Meanwhile, the training time of global model for the proposed approximation algorithm is very close to that for optimal solution generated by the brute-force approach for all cases. Besides, the integrated algorithm outperforms the existing works when the available storage capacity varies during the training. [ABSTRACT FROM AUTHOR]

We study the Generalized Min Sum Set Cover (GMSSC) problem, wherein given a collection of hyperedges E with arbitrary covering requirements { ke Z + : e Ⲉ E}, the goal is to find an ordering of the vertices to minimize the total cover time of the hyperedges; a hyperedge e is considered covered by the first time when ke and many of its vertices appear in the ordering. We give a 4.642 approximation algorithm for GMSSC, coming close to the best possible bound of 4, already for the classical special case (with all ke = 1) of Min Sum Set Cover (MSSC) studied by Feige, Lovász, and Tetali, and improving upon the previous best known bound of 12.4 due to Im, Sviridenko, and van der Zwaan. Our algorithm is based on transforming the LP solution by a suitable kernel and applying randomized rounding. As part of the analysis of our algorithm, we also derive an inequality on the lower tail of a sum of independent Bernoulli random variables, which might be of independent interest and broader utility. Min Sum Vertex Cover (MSVC) is a well-known special case of MSSC in which the input hypergraph is a graph (i.e., | e| = 2) and ke = 1 for every edge e E. We give a 16/9 ≃ 1.778 approximation for MSVC and show a matching integrality gap for the natural LP relaxation. This improves upon the previous best 1.999946 approximation of Barenholz, Feige, and Peleg. Finally, we revisit MSSC and consider the lp norm of cover-time of the hyperedges. Using a dual fitting argument, we show that the natural greedy algorithm achieves tight, up to NP-hardness, approximation guarantees of (p + 1)1+1/p for all p ≥ 1, giving another proof of the result of Golovin, Gupta, Kumar, and Tangwongsan, and showing its tightness up to NP-hardness. For p = 1, this gives yet another proof of the 4 approximation for MSSC. [ABSTRACT FROM AUTHOR]

In the directed Steiner tree (DST) problem, we are given an n-vertex directed edgeweighted graph, a root r, and a collection of k terminal nodes. Our goal is to find a minimum-cost subgraph that contains a directed path from r to every terminal. We present an O(log² k/ log log k)- approximation algorithm for DST that runs in quasi-polynomial time, i.e., in time n poly log(k) . By assuming the projection game conjecture and NP ¢n0<ε<1 ZPTIME(2nε ) and adjusting the parameters in the hardness result of [Halperin and Krauthgamer, Polylogarithmic inapproximability, in Proceedings of the 35th Annual ACM Symposium on Theory of Computing, 2003, pp. 585--594], we show the matching lower bound of Ω (log² k/ log log k) for the class of quasi-polynomial time algorithms, meaning that our approximation ratio is asymptotically the best possible. Our algorithm is proceeded by reducing DST to an intermediate problem, namely, the group Steiner tree on trees with dependency constraint problem, which we approximate using the framework developed by [Rothvo{\ss}, Directed Steiner Tree and the Lasserre Hierarchy, preprint, arxiv:1111.5473, 2011] and [Friggstad et al., Linear programming hierarchies suffice for directed Steiner tree, in Proceedings of the 17th Annual Conference on Integer Programming and Combinatorial Optimization, 2014, pp. 285--296]. [ABSTRACT FROM AUTHOR]

We give a 2-approximation algorithm for the Maximum Agreement Forest problem on two rooted binary trees. This NP-hard problem has been studied extensively in the past two decades, since it can be used to compute the rooted Subtree Prune-and-Regraft (rSPR) distance between two phylogenetic trees. Our algorithm is combinatorial and its running time is quadratic in the input size. To prove the approximation guarantee, we construct a feasible dual solution for a novel exponential-size linear programming formulation. In addition, we show this linear program has a smaller integrality gap than previously known formulations, and we give an equivalent compact formulation, showing that it can be solved in polynomial time. [ABSTRACT FROM AUTHOR]

We introduce and study a discrete multi-period extension of the classical knapsack problem, dubbed generalized incremental knapsack. In this setting, we are given a set of n items, each associated with a non-negative weight, and T time periods with non-decreasing capacities W 1 ≤ ⋯ ≤ W T . When item i is inserted at time t, we gain a profit of p it ; however, this item remains in the knapsack for all subsequent periods. The goal is to decide if and when to insert each item, subject to the time-dependent capacity constraints, with the objective of maximizing our total profit. Interestingly, this setting subsumes as special cases a number of recently-studied incremental knapsack problems, all known to be strongly NP-hard. Our first contribution comes in the form of a polynomial-time (1 2 - ϵ) -approximation for the generalized incremental knapsack problem. This result is based on a reformulation as a single-machine sequencing problem, which is addressed by blending dynamic programming techniques and the classical Shmoys–Tardos algorithm for the generalized assignment problem. Combined with further enumeration-based self-reinforcing ideas and new structural properties of nearly-optimal solutions, we turn our algorithm into a quasi-polynomial time approximation scheme (QPTAS). Hence, under widely believed complexity assumptions, this finding rules out the possibility that generalized incremental knapsack is APX-hard. [ABSTRACT FROM AUTHOR]

In the paper, we design an adaptive algorithm for non-submodular set function maximization over a single matroid constraint. We measure the deviation of the set function from fully submodular with the help of the generic submodularity ratio γ. The adaptivity quantifies the information theoretic complexity of oracle optimization for parallel computations. We propose a new approximation algorithm based on the continuous greedy approach and prove that the algorithm could obtain a fractional solution with approximation ratio (1 -- ... -- O(ϵ)) in O(log n log(k/γϵ)/ϵ-2 log n log(1/γ)--ϵ-1log(1--ϵ) adaptive rounds. We then use the contention resolution schemes to convert the fractional solution to a discrete one with γ(1 -- e-1)(1 -- ... -- O(ϵ))-approximation. [ABSTRACT FROM AUTHOR]

The Unsplittable Flow Cover problem (UFP-cover) models the well-studied general caching problem and various natural resource allocation settings. We are given a path with a demand on each edge and a set of tasks, each task being defined by a subpath and a size. The goal is to select a subset of the tasks of minimum cardinality such that on each edge e the total size of the selected tasks using e is at least the demand of e. There is a polynomial time 4-approximation for the problem (Bar-Noy et al. STOC 2001) and also a QPTAS (Höhn et al. ICALP 2018). In this paper we study fixed-parameter algorithms for the problem. We show that it is W[1]-hard but it becomes FPT if we can slighly violate the edge demands (resource augmentation) and also if there are at most k different task sizes. Then we present a parameterized approximation scheme (PAS), i.e., an algorithm with a running time of f (k) ⋅ n O 휖 (1) that outputs a solution with at most (1 + 휖)k tasks or asserts that there is no solution with at most k tasks. In this algorithm we use a new trick that intuitively allows us to pretend that we can select tasks from OPT multiple times. We show that the other two algorithms extend also to the weighted case of the problem, at the expense of losing a factor of 1 + 휖 in the cost of the selected tasks. [ABSTRACT FROM AUTHOR]

While the basic greedy algorithm gives a semi-streaming algorithm with an approximation guarantee of 2 for the unweighted matching problem, it was only recently that Paz and Schwartzman obtained an analogous result for weighted instances. Their approach is based on the versatile local ratio technique and also applies to generalizations such as weighted hypergraph matchings. However, the framework for the analysis fails for the related problem of weighted matroid intersection and as a result the approximation guarantee for weighted instances did not match the factor 2 achieved by the greedy algorithm for unweighted instances.Our main result closes this gap by developing a semi-streaming algorithm with an approximation guarantee of 2 + ε for weighted matroid intersection, improving upon the previous best guarantee of 4 + ε . Our techniques also allow us to generalize recent results by Levin and Wajc on submodular maximization subject to matching constraints to that of matroid-intersection constraints. While our algorithm is an adaptation of the local ratio technique used in previous works, the analysis deviates significantly and relies on structural properties of matroid intersection, called kernels. Finally, we also conjecture that our algorithm gives a (k + ε) approximation for the intersection of k matroids but prove that new tools are needed in the analysis as the structural properties we use fail for k ≥ 3 . [ABSTRACT FROM AUTHOR]

We consider the graph k-partitioning problem under the min-max objective, termed as Minmax k -cut. The input here is a graph G = (V , E) with non-negative integral edge weights w : E → Z + and an integer k ≥ 2 and the goal is to partition the vertices into k non-empty parts V 1 , ... , V k so as to minimize max i = 1 k w (δ (V i)) . Although minimizing the sum objective ∑ i = 1 k w (δ (V i)) , termed as Minsum k -cut, has been studied extensively in the literature, very little is known about minimizing the max objective. We initiate the study of Minmax k -cut by showing that it is NP-hard and W[1]-hard when parameterized by k, and design a parameterized approximation scheme when parameterized by k. The main ingredient of our parameterized approximation scheme is an exact algorithm for Minmax k -cut that runs in time (λ k) O (k 2) n O (1) + O (m) , where λ is value of the optimum, n is the number of vertices, and m is the number of edges. Our algorithmic technique builds on the technique of Lokshtanov, Saurabh, and Surianarayanan (FOCS, 2020) who showed a similar result for Minsum k -cut. Our algorithmic techniques are more general and can be used to obtain parameterized approximation schemes for minimizing ℓ p -norm measures of k-partitioning for every p ≥ 1 . [ABSTRACT FROM AUTHOR]

We give the first 2-approximation algorithm for the cluster vertex deletion problem. This approximation factor is tight, since approximating the problem within any constant factor smaller than 2 is UGC-hard. Our algorithm combines previous approaches, based on the local ratio technique and the management of twins, with a novel construction of a "good" cost function on the vertices at distance at most 2 from any vertex of the input graph. As an additional contribution, we also study cluster vertex deletion from the polyhedral perspective, where we prove almost matching upper and lower bounds on how well linear programming relaxations can approximate the problem. [ABSTRACT FROM AUTHOR]

We investigate offline and online algorithms for Round - UFPP , the problem of minimizing the number of rounds required to schedule a set of unsplittable flows of non-uniform size on a given path with heterogeneous edge capacities. Round - UFPP is known to be NP-hard and there are constant-factor approximation algorithms under the no bottleneck assumption (NBA), which stipulates that maximum size of any flow is at most the minimum global edge capacity. In this work, we present improved online and offline algorithms for Round - UFPP without the NBA. We first study offline Round - UFPP for a restricted class of instances, called α -small, where the size of each flow is at most α times the capacity of its bottleneck edge, and present an O (log (1 / (1 - α))) -approximation algorithm. Next, our main result is an online O (log log c max) -competitive algorithm for Round - UFPP where c max is the largest edge capacity, improving upon the previous best bound of O (log c max) due to Epstein et al. (SIAM J Discrete Math 23(2):822–841, 2009). These new results lead to an offline O (min (log n , log m , log log c max)) -approximation algorithm and an online O (min (log m , log log c max)) -competitive algorithm for Round - UFPP , where n is the number of flows and m is the number of edges. [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]

In this paper, we devise improved approximation algorithms for the Min–Max Rural Postmen Cover Problem (RuralPostCover) and the Min–Max Chinese Postmen Cover Problem (ChinesePostCover), which are natural extensions of the classical Rural Postman Problem and the Chinese Postman Problem where multiple postmen are available. These results are based on some key observations, a new approach to derive closed walks from (open) walks and an efficient postmen allocation procedure in the literature. As an application of the algorithm for RuralPostCover, we give the first constant-factor approximation algorithms for the Min–Max Subtree Cover Problem (SubtreeCover) and its generalization, called the Min–Max Steiner Tree Cover Problem with Vertex Weights (SteinerTreeCover), using simple approximation preserving reductions. Moreover, we devise specialized algorithms for SteinerTreeCover (SubtreeCover) with better approximation ratios. [ABSTRACT FROM AUTHOR]

We present a new approximation algorithm for the minimum 2-edge-connected spanning subgraph problem. Its approximation ratio is 4 3 , which matches the current best ratio. The approximation ratio of the algorithm is 6 5 on subcubic graphs, which is an improvement upon the previous best ratio of 5 4. The algorithm is a novel extension of the primal-dual schema, which consists of two distinct phases. Both the algorithm and the analysis are much simpler than those of the previous approaches. [ABSTRACT FROM AUTHOR]

The squared metric k -facility location problem is a frequently encountered generalization of the k -means problem, where a specific cost should be paid for opening each facility. The current best approximation ratio for this problem is 44.473 + ϵ , which was obtained using a local search algorithm. We advance the state-of-the-art for the problem by devising a Lagrangian relaxation-based algorithm that achieves an improved approximation guarantee of 36.342 + ϵ. Our improvement comes from a new deterministic rounding approach, which exploits the properties of the squared metric. • We give a (36.342 + ϵ) -approximation algorithm for the squared metric k -facility location problem. • We obtain a well-behaved fractional solution to the squared metric k -facility location problem based on the framework of Lagrangian relaxation. • We give a new deterministic rounding approach that exploits the properties of the squared metric. [ABSTRACT FROM AUTHOR]

This work considers the Minimum Path-Collection Exact Cover (PCEC) and the Minimum k -Path Splitting Exact Cover (k-PSEC). Both problems receive a digraph G and a set P of paths in G , and their objective is to find a minimum cardinality set S of paths, whose elements are arc-disjoint and cover all arcs of G. Despite the similarities, the solutions for each problem must satisfy different properties. For k-PSEC , the set S must be obtained by splitting the paths in P in order to guarantee that no element of S has length greater than a given integer k. For PCEC , the paths in P cannot be split, and the elements of S are single arcs of G or complete paths of P. PCEC and k-PSEC have practical applications in network design and network monitoring systems, being also natural versions of graph covering problems. However, there are no theoretical studies on their complexity. This work not only presents NP-hardness results for the problems, but also proves that, unless P = NP , PCEC cannot be | P | O (1) -approximated in polynomial-time. Moreover, polynomial-time algorithms are presented for paths, cycles, and trees, and polynomial-time approximation algorithms are proposed for special cases of k-PSEC. [ABSTRACT FROM AUTHOR]

The tensor-train (TT) format is a highly compact low-rank representation for highdimensional tensors. TT is particularly useful when representing approximations to the solutions of certain types of parametrized partial differential equations. For many of these problems, computing the solution explicitly would require an infeasible amount of memory and computational time. While the TT format makes these problems tractable, iterative techniques for solving the PDEs must be adapted to perform arithmetic while maintaining the implicit structure. The fundamental operation used to maintain feasible memory and computational time is called rounding, which truncates the internal ranks of a tensor already in TT format. We propose several randomized algorithms for this task that are generalizations of randomized low-rank matrix approximation algorithms and provide significant reduction in computation compared to deterministic TT-rounding algorithms. Randomization is particularly effective in the case of rounding a sum of TT-tensors (where we observe 20\times speedup), which is the bottleneck computation in the adaptation of GMRES to vectors in TT format. We present the randomized algorithms and compare their empirical accuracy and computational time with deterministic alternatives. [ABSTRACT FROM AUTHOR]

We introduce a streaming framework for analyzing stochastic approximation/optimization problems. This streaming framework is analogous to solving optimization problems using time-varying mini-batches that arrive sequentially. We provide non-asymptotic convergence rates of various gradientbased algorithms; this includes the famous Stochastic Gradient (SG) descent (a.k.a. Robbins-Monro algorithm), mini-batch SG and time-varying mini-batch SG algorithms, as well as their iterated averages (a.k.a. Polyak-Ruppert averaging). We show (i) how to accelerate convergence by choosing the learning rate according to the time-varying mini-batches, (ii) that Polyak-Ruppert averaging achieves optimal convergence in terms of attaining the Cramer-Rao lower bound, and (iii) how time-varying mini-batches together with Polyak-Ruppert averaging can provide variance reduction and accelerate convergence simultaneously, which is advantageous for many learning problems, such as online, sequential, and large-scale learning. We further demonstrate these favorable effects for various time-varying minibatches. [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]

We give better approximation ratios for two Steiner Tree variants by combining known algorithms: the optimum 3 -decomposition and iterative randomized rounding. The first problem is Steiner Tree with minimum number of Steiner points and bounded edge length problem ( S M T - M S P ). The input consists of a set of terminals R in the Euclidean space R 2 . A feasible solution is a Steiner tree τ spanning R with Steiner points S such that every edge in τ has length at most 1 . The objective is to minimize S . Previously, the best approximation ratio for S M T - M S P was 1 + ln (4) + ϵ ≈ 2.386 . We present a polynomial time algorithm with ratio 2.277 . The second problem is Steiner Tree in quasi-bipartite graphs. It is a Steiner Tree problem on graph G = (V , E , c) with terminal set R when the edge set E does not include any edge between two vertices in V \ R . The best-known approximation ratio for this problem is 73 60 , We improve this ratio to 298 245 . [ABSTRACT FROM AUTHOR]

We study geometric duality for convex vector optimization problems. For a primal problem with a q-dimensional objective space, we formulate a dual problem with a (q+1)-dimensional objective space. Consequently, different from an existing approach, the geometric dual problem does not depend on a fixed direction parameter, and the resulting dual image is a convex cone. We prove a one-to-one correspondence between certain faces of the primal and dual images. In addition, we show that a polyhedral approximation for one image gives rise to a polyhedral approximation for the other. Based on this, we propose a geometric dual algorithm which solves the primal and dual problems simultaneously and is free of direction-biasedness. We also modify an existing direction-free primal algorithm in such a way that it solves the dual problem as well. We test the performance of the algorithms for randomly generated problem instances by using the so-called primal error and hypervolume indicator as performance measures. [ABSTRACT FROM AUTHOR]

We study the problem of computing the p q norm of a matrix A ∈ Rm×n, defined as ∣∣j4∣∣p-g = maxx∈Rn{0}'.||Ax|q/||x|p This problem generalizes the spectral norm of a matrix (p = q = 2) and the Grothendieck problem (p = ∞, q = 1) and has been widely studied in various regimes. When p ≥ q, the problem exhibits a dichotomy: constant factor approximation algorithms are known if 2 ∈ [g,p], and the problem is hard to approximate within almost polynomial factors when 2 [g,p]. The regime when p < q, known as Hypercontractive norms, is particularly significant for various applications but much less well understood. The case with p = 2 and q > 2 was studied by Barak et al. [Proceedings of the 4Ath Annual ACM Symposium on Theory of Computing, 2012, pp. 307--326], who gave subexponential algorithms for a promise version of the problem (which captures small-set expansion) and also proved hardness of approximation results based on the exponential time hypothesis. However, no NP-hardness of approximation is known for these problems for any p < q. We prove the first NP-hardness result (under randomized reductions) for approximating hypercontractive norms. We show that for any 1 < p < q < ∞ with 2 [p, g], ∣∣√4∣∣p--q is hard to approximate within 2°(log n)1-x) assuming NP g BPTIME(21log n A-). En rθute to the above result, we also prove almost tight results for the case when p > q with 2 ∈ [q, p]. [ABSTRACT FROM AUTHOR]

The terminal backup problems ([E. Anshelevich and A. Karagiozova, SIAM J. Comput., 40 (2011), pp. 678--708]) form a class of network design problems: Given an undirected graph with a requirement on terminals, the goal is to find a minimum-cost subgraph satisfying the connectivity requirement. The node-connectivity terminal backup problem requires a terminal to connect other terminals with a number of node-disjoint paths. This problem is not known whether is NP-hard or tractable. Fukunaga [SIAM J. Discrete Math., 30 (2016), pp. 777--800] gave a 4/3-approximation algorithm based on an LP-rounding scheme using a general LP-solver. In this paper, we develop a combinatorial algorithm for the relaxed LP to find a half-integral optimal solution in O(mlog(n-A · MF(/cn,m T/c2n)) time, where n is the number of nodes, m is the number of edges, k is the number of terminals, A is the maximum edge-cost, U is the maximum edge-capacity, and MF(nz,mz) is the time complexity of a max-flow algorithm in a network with nz nodes and m' edges. The algorithm implies that the 4/3-approximation algorithm for the node-connectivity terminal backup problem is also efficiently implemented. For the design of algorithm, we explore a connection between the node-connectivity terminal backup problem and a new type of a multiflow, which is called a separately capacitated multiflow. We show a min-max theorem which extends the Lovasz-Cherkassky theorem to the node-capacity setting. Our results build on discrete convexity in the node-connectivity terminal backup problem. [ABSTRACT FROM AUTHOR]

This paper deals with an analysis of three algorithms for the graph vertex cover problem. Certain methods for solving this problem are analyzed. In addition, different studies on the problem and some approaches to its solution are discussed as well. An exact algorithm (based on the backtracking approach) is presented. Calculating the average time for execution of this algorithm is consistent with the multitasking way of work of the operating system. For this purpose, four different starts of the algorithm are made and then the average time of all of them is calculated. The exact algorithm found the optimal solutions for all analyzed graphs. Besides this algorithm, two other heuristic algorithms for solving the problem are discussed. For this study, an interactive application is developed to visualize the performance of the three algorithms and display the obtained results. The results show that for small graphs with no more than 25 vertices, the exact algorithm can be used to solve optimally the graph vertex cover problem. For the largest graphs, none of the two heuristic algorithms found the optimal solutions, but these algorithms generated solutions that are very close to the optimal ones. In summary, when the size of the graph increases linearly, the execution time of the heuristic algorithms increases linearly, while the execution time of the exact algorithm increases exponentially. [ABSTRACT FROM AUTHOR]

Collective graphical model (CGM) is a probabilistic model that provides a framework for analyzing aggregated count data. Maximum a posteriori (MAP) inference of unobserved variables under given observations is one of the essential operations in CGM. Because the MAP inference problem is known to be NP-hard in general, the current mainstream approach is to solve an alternative problem obtained by approximating the objective function and applying continuous relaxation. However, this approach has two significant drawbacks. First, the quality of the solution deteriorates when the values in the count data are negligible due to the inaccuracy of Stirling's approximation. Second, the application of continuous relaxation causes the violation of integrality constraints. This paper proposes novel algorithms for MAP inference in CGMs on path graphs to overcome these problems. Our method is based on the discrete difference of convex algorithm (DCA); DCA is a general framework to minimize the sum of a convex function and a concave function by repeatedly minimizing surrogate functions. Utilizing the particular structure of path graphs, we efficiently solve the surrogate function minimization by minimum convex cost flow algorithms. Furthermore, our approach also leads to a new method of solving another important task; MAP inference of the sample size in CGM on path graphs. Our method is naturally applicable to this task, allowing us to design very efficient algorithms. Experimental results on synthetic and real-world datasets show the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Absence of (complex) zeros property is at the heart of the interpolation method developed by Barvinok for designing deterministic approximation algorithms for various graph counting and related problems. An earlier method used for the same problem is one based on the correlation decay property. Remarkably, the classes of graphs for which the two methods apply often coincide or nearly coincide. In this article we show that this is not a coincidence. We establish that if the interpolation method is valid for a family of graphs, then this family exhibits a form of the correlation decay property which is asymptotic strong spatial mixing at superlogarithmic distances. Our proof is based on a certain graph polynomial representation of the associated partition function. This representation is at the heart of the design of the polynomial time algorithms underlying the interpolation method itself. We conjecture that our result holds for all, and not just amenable graphs. Indeed this conjecture was recently confirmed by Regts. See the body of the article for details. [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]

The traditional relay deployment problem typically assumes that the locations of users are known and stationary, which is not realistic in practice. The prevalence of mobile devices has made it possible to collect user trajectory and account for user movement while deploying relays. Under this background, a novel problem trajectory-based relay deployment (TBRD) is put forward. This problem considers communication-related metrics and is aimed at maximizing user connection time as users roam through the target area under relay resource constraints, which is more reasonable than the goal of expanding the relay coverage. To figure out the TBRD, we first propose the concept demand nodes (DNs), which are virtual weighted nodes representing the locations where users frequently pass or stay for a long period. Next, we design a Demand Node Generation algorithm that can transform the continuous historical user trajectory into a number of discrete DNs. By generating DNs, we convert the TBRD problem into a demand node coverage (DNC) problem, which is proved to be NP-complete. Followed by that, we introduce an approximation algorithm, named Submodular Iterative Deployment Algorithm , which solves the DNC problem with the approximation factor |$1-\frac{1}{\sqrt{e\cdot (1-1/k)}}$|⁠ , where |$e$| is the mathematical constant, and |$k$| is the relay number constraint. Finally, five real trajectory datasets are used to evaluate our proposed algorithm, and the simulation results demonstrate that our algorithm can obtain high coverage for users in motion, which can lead to better user experience. In addition, we also analyze the impact of different parameters on the coverage performance, and under this circumstance, we may safely come to the conclusion that our work is at the leading edge to utilize user trajectories for relay deployment in wireless networks. [ABSTRACT FROM AUTHOR]

Tverberg's theorem states that for any k ≥ 2 and any set P ⊂ R d of at least (d + 1) (k - 1) + 1 points in d dimensions, we can partition P into k subsets whose convex hulls have a non-empty intersection. The associated search problem of finding the partition lies in the complexity class CLS = PPAD ∩ PLS , but no hardness results are known. In the colorful Tverberg theorem, the points in P have colors, and under certain conditions, P can be partitioned into colorful sets, in which each color appears exactly once and whose convex hulls intersect. To date, the complexity of the associated search problem is unresolved. Recently, Adiprasito, Bárány, and Mustafa (SODA 2019) gave a no-dimensional Tverberg theorem, in which the convex hulls may intersect in an approximate fashion. This relaxes the requirement on the cardinality of P. The argument is constructive, but does not result in a polynomial-time algorithm. We present a deterministic algorithm that finds for any n-point set P ⊂ R d and any k ∈ { 2 , ⋯ , n } in O (n d ⌈ log k ⌉) time a k-partition of P such that there is a ball of radius O ((k / n) diam (P)) that intersects the convex hull of each set. Given that this problem is not known to be solvable exactly in polynomial time, our result provides a remarkably efficient and simple new notion of approximation. Our main contribution is to generalize Sarkaria's method (Israel Journal Math., 1992) to reduce the Tverberg problem to the colorful Carathéodory problem (in the simplified tensor product interpretation of Bárány and Onn) and to apply it algorithmically. It turns out that this not only leads to an alternative algorithmic proof of a no-dimensional Tverberg theorem, but it also generalizes to other settings such as the colorful variant of the problem. [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]