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The Industrial Internet of Things (IIoT) envisions enhanced surveillance and control for industrial applications through diverse IoT devices. However, the increasing heterogeneity of deployed end devices poses challenges to current practices, hampering overall performance as device numbers escalate. To tackle this issue, we introduce an innovative distributed power control algorithm leveraging the wireless channel's nature to approximate the centralized maximum-weight scheduling algorithm. Employing ubiquitous multi-protocol mobile devices as intermediaries, we propose a concurrent dual-hop/multi-hop backhauling strategy, improving interoperability and facilitating data relay, translation, and forwarding from end IoT devices. Our focus is directed towards addressing large-scale network stability and queue management challenges. We formulate a long-term time-averaged optimization problem, incorporating considerations of end-to-end rate control, routing, link scheduling, and resource allocation to guarantee essential network-wide throughput. Furthermore, we present a real-time decomposition-based approximation algorithm that ensures adaptive resource allocation, queue stability, and meeting Quality of Service (QoS) constraints with the highest energy efficiency. Comprehensive numerical results verify significant energy efficiency improvements across diverse traffic models, maintaining throughput requirements for both uniform and hotspot User Equipment (UE) distribution patterns. This work offers a comprehensive solution to enhance IIoT performance and address evolving challenges in industrial applications. [ABSTRACT FROM AUTHOR]

In MAXSPACE, given a set of ads A , one wants to schedule a subset A ′ ⊆ A into K slots B 1 , ⋯ , B K of size L. Each ad A i ∈ A has a size s i and a frequency w i . A schedule is feasible if the total size of ads in any slot is at most L, and each ad A i ∈ A ′ appears in exactly w i slots and at most once per slot. The goal is to find a feasible schedule that maximizes the sum of the space occupied by all slots. We consider a generalization called MAXSPACE-R for which an ad A i also has a release date r i and may only appear in a slot B j if j ≥ r i . For this variant, we give a 1/9-approximation algorithm. Furthermore, we consider MAXSPACE-RDV for which an ad A i also has a deadline d i (and may only appear in a slot B j with r i ≤ j ≤ d i ), and a value v i that is the gain of each assigned copy of A i (which can be unrelated to s i ). We present a polynomial-time approximation scheme for this problem when K is bounded by a constant. This is the best factor one can expect since MAXSPACE is strongly NP-hard, even if K = 2 . [ABSTRACT FROM AUTHOR]

This work studies solutions to determine the macro-elastic moduli of three-phase composite materials with imperfect interfaces in 2D. Which is based on the coated circular assemblage model of Hashin-Strikman and the polarization approximation method (PA) to develop the formulae for elastic moduli of circle inclusions with spring-layer and surface-stress imperfect interfaces. From that, explicit algebraic expressions were obtained to estimate the elastic moduli of three-phase composites with imperfect interfaces, in which two phases are different with circular inclusions distributed randomly in the matrix. Besides, the FFT algorithm and the differential approximation (DA) are also developed to determine the elastic moduli of the three-phase composite with imperfect interfaces. The results of the FFT numerical methods will be compared with the DA and PA results with different material cases to show the effectiveness of the applied methods. [ABSTRACT FROM AUTHOR]

Many modern day cloud hosted applications such as virtual reality, real time games require low latency data access and computation to improve response time. So it is essential to bring the computation and data storage edge servers closer to the user's geographical location to improve response times and save bandwidth. In particulars, in online gaming and on demand video services, the required application data present at cloud servers need to be placed on the edge servers to provide low latency app-functionalities. The transfer of huge amount of data from cloud server to edge server incurs high cost and time penalties. Thus, we need an efficient way to solve edge data distribution (EDD) problem which distribute the application data to the edge servers that minimizes transfer cost. In this work, we provide a refined formulation of an optimal approach to solve the EDD problem using integer linear programming (ILP) technique. Due to the time complexity limitation of the ILP approach, we propose an O(k) approximation algorithm based on network Steiner tree estimation (EDD-NSTE) for estimating solutions to dense large-scale EDD problem. The proposed approach is analyzed to be 11/6 approximation which is better than the state-of-the-art 2 approximation EDD-A approach. The experimental evaluation through simulation using real world EUA data set demonstrate that the EDD-NSTE outperform state-of-the-art approach and other representative approaches. [ABSTRACT FROM AUTHOR]

In offline scheduling models, jobs are given with their exact processing times. In their online counterparts, jobs arrive in sequence together with their processing times and the scheduler makes irrevocable decisions on how to execute each of them upon its arrival. We consider a semi-online variant which has equally rich application background, called scheduling with testing, where the exact processing time of a job is revealed only after a required testing operation is finished, or otherwise the job has to be executed for a given possibly over-estimated length of time. For multiprocessor scheduling with testing to minimize the total job completion time, we present several first approximation algorithms with constant competitive ratios for various settings, including a 2 φ -competitive algorithm for the non-preemptive general testing case and a (0.0382 + 2.7925 (1 - 1 2 m)) -competitive randomized algorithm, when the number of machines m ≥ 37 or otherwise 2.7925-competitive, where φ = (1 + 5) / 2 < 1.6181 is the golden ratio and m is the number of machines, a (3.5 - 3 2 m) -competitive algorithm allowing job preemption when m ≥ 3 or otherwise 3-competitive, and a (φ + φ + 1 2 (1 - 1 m)) -competitive algorithm for the non-preemptive uniform testing case when m ≥ 5 or otherwise (φ + 1) -competitive. Our results improve three previous best approximation algorithms for the single machine scheduling with testing problems, respectively. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of finding a regression in a version control system (VCS), such as git. The set of versions is modelled by a directed acyclic graph (DAG) where vertices represent versions of the software, and arcs are the changes between different versions. We assume that somewhere in the DAG, a bug was introduced, which persists in all of its subsequent versions. It is possible to query a vertex to check whether the corresponding version carries the bug. Given a DAG and a bugged vertex, the Regression Search Problem consists in finding the first vertex containing the bug in a minimum number of queries in the worst-case scenario. This problem is known to be NP-complete. We study the algorithm used in git to address this problem, known as git bisect. We prove that in a general setting, git bisect can use an exponentially larger number of queries than an optimal algorithm. We also consider the restriction where all vertices have indegree at most 2 (i.e. where merges are made between at most two branches at a time in the VCS), and prove that in this case, git bisect is a 1 log 2 (3 / 2) -approximation algorithm, and that this bound is tight. We also provide a better approximation algorithm for this case. Finally, we give an alternative proof of the NP-completeness of the Regression Search Problem, via a variation with bounded indegree. [ABSTRACT FROM AUTHOR]

In this paper we study the classical problem of throughput maximization. In this problem we have a collection J of n jobs, each having a release time r j , deadline d j , and processing time p j . They have to be scheduled non-preemptively on m identical parallel machines. The goal is to find a schedule which maximizes the number of jobs scheduled entirely in their [ r j , d j ] window. This problem has been studied extensively (even for the case of m = 1 ). Several special cases of the problem remain open. Bar-Noy et al. (Proceedings of the Thirty-First Annual ACM Symposium on Theory of Computing, May 1–4, 1999, Atlanta, Georgia, USA, pp. 622–631. ACM, 1999, https://doi.org/10.1145/301250.301420) presented an algorithm with ratio 1 - 1 / (1 + 1 / m) m for m machines, which approaches 1 - 1 / e as m increases. For m = 1 , Chuzhoy et al. (42nd Annual Symposium on Foundations of Computer Science (FOCS) 2001, 14–17 October 2001, Las Vegas, Nevada, USA, pp. 348–356. IEEE Computer Society, 2001) presented an algorithm with approximation with ratio 1 - 1 e - ε (for any ε > 0 ). Recently Im et al. (SIAM J Discrete Math 34(3):1649–1669, 2020) presented an algorithm with ratio 1 - 1 / e + ε 0 for some absolute constant ε 0 > 0 for any fixed m. They also presented an algorithm with ratio 1 - O (log m / m) - ε for general m which approaches 1 as m grows. The approximability of the problem for m = O (1) remains a major open question. Even for the case of m = 1 and c = O (1) distinct processing times the problem is open (Sgall in: Algorithms - ESA 2012 - 20th Annual European Symposium, Ljubljana, Slovenia, September 10–12, 2012. Proceedings, pp 2–11, 2012). In this paper we study the case of m = O (1) and show that if there are c distinct processing times, i.e. p j 's come from a set of size c, then there is a randomized (1 - ε) -approximation that runs in time O (n m c 7 ε - 6 log T) , where T is the largest deadline. Therefore, for constant m and constant c this yields a PTAS. Our algorithm is based on proving structural properties for a near optimum solution that allows one to use a dynamic programming with pruning. [ABSTRACT FROM AUTHOR]

Stochastic optimization has experienced significant growth in recent decades, with the increasing prevalence of variance reduction techniques in stochastic optimization algorithms to enhance computational efficiency. In this paper, we introduce two projection-free stochastic approximation algorithms for maximizing diminishing return (DR) submodular functions over convex constraints, building upon the Stochastic Path Integrated Differential EstimatoR (SPIDER) and its variants. Firstly, we present a SPIDER Continuous Greedy (SPIDER-CG) algorithm for the monotone case that guarantees a (1 - e - 1) OPT - ε approximation after O (ε - 1) iterations and O (ε - 2) stochastic gradient computations under the mean-squared smoothness assumption. For the non-monotone case, we develop a SPIDER Frank–Wolfe (SPIDER-FW) algorithm that guarantees a 1 4 (1 - min x ∈ C ‖ x ‖ ∞) OPT - ε approximation with O (ε - 1) iterations and O (ε - 2) stochastic gradient estimates. To address the practical challenge associated with a large number of samples per iteration, we introduce a modified gradient estimator based on SPIDER, leading to a Hybrid SPIDER-FW (Hybrid SPIDER-CG) algorithm, which achieves the same approximation guarantee as SPIDER-FW (SPIDER-CG) algorithm with only O (1) samples per iteration. Numerical experiments on both simulated and real data demonstrate the efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]

We investigate the seemingly untouched yet the most general parallel identical k-stage flow-shops scheduling, in which we are given an arbitrary number of indistinguishable k-stage flow-shops and a set of jobs each to be processed on one of the flow-shops, and the goal is to schedule these jobs to the flow-shops so as to minimize the makespan. Here the number k of stages is a fixed constant, but the number of flow-shops is part of the input. This scheduling problem is strongly NP-hard. To the best of our knowledge all previously presented approximation algorithms are for the special case where k = 2 , including a 17/6-approximation in 2017, a (2 + ϵ) -approximation in 2018, and the most recent polynomial-time approximation scheme in 2020; they all take advantage of the number of stages being two. We deal with an arbitrary constant k ≥ 3 , where the k-stage flow-shop scheduling is already strongly NP-hard. To define a configuration that summarizes the key information about the job assignments in a feasible schedule, we present novel concepts of big job type, big job assignment pair type, and flow-shop type. We show that the total number of distinct configurations is a polynomial in the input number of flow-shops. We then present how to compute a schedule for each configuration that assigns all the big jobs, followed by how to allocate all the small jobs into the schedule at a cost only a fraction of the makespan. These together lead to a polynomial-time approximation scheme for the problem. [ABSTRACT FROM AUTHOR]

In 2015, Haviv introduced the Remote set problem (RSP) and studied the complexity of the covering radius problem (CRP), which is a classical problem in lattices. The RSP aims to identify a set containing a point that is sufficiently distant from a given lattice L . It introduced a new method for analyzing the complexity of CRP. An open question in RSP is whether we can obtain the approximation factor γ = 1 / 2 . This paper investigates this question and proposes a probabilistic polynomial-time algorithm for RSP with an approximation factor of 1 / 2 - 1 / (c λ n (p)) , where c ∈ Z + and λ n (p) is the n-th successive minima in lattice under l p -norm. For a given lattice L with rank n and positive integer d, our algorithm outputs a set S of size d in polynomial time. This set S includes a point at least (1 2 - 1 c λ n (p) ) ρ (p) (L) from lattice L with a probability greater than 1 - 1 / 2 d . Here, c is a positive integer and ρ (p) (L) denotes the covering radius of L in l p -norm( 1 ≤ p ≤ ∞ ). Based on this, we obtain that GAPCRP 2 + 1 / 2 O (n) belongs to the complexity class coRP, and we provide new reductions from GAPCRP to GAPCVP. [ABSTRACT FROM AUTHOR]

In this work, we introduce a multi-vehicle (or multi-postman) extension of the classical Mixed Rural Postman Problem, which we call the Min–Max Mixed Rural Postmen Cover Problem (MRPCP). The MRPCP is defined on a mixed graph G = (V , E , A) , where V is the vertex set, E denotes the (undirected) edge set and A represents the (directed) arc set. Let F ⊆ E ( H ⊆ A ) be the set of required edges (required arcs). There is a nonnegative weight associated with each edge and arc. The objective is to determine no more than k closed walks to cover all the required edges in F and all the required arcs in H such that the weight of the maximum weight closed walk is minimized. By replacing closed walks with (open) walks in the MRPCP, we obtain the Min–Max Mixed Rural Postmen Walk Cover Problem (MRPWCP). The Min–Max Mixed Chinese Postmen Cover Problem (MCPCP) is a special case of the MRPCP where F = E and H = A . The Min–Max Stacker Crane Cover Problem (SCCP) is another special case of the MRPCP where F = ∅ and H = A For the MRPCP with the input graph satisfying the weakly symmetric condition, i.e., for each arc there exists a parallel edge whose weight is not greater than this arc, we devise a 27 4 -approximation algorithm. This algorithm achieves an approximation ratio of 33 5 for the SCCP with the weakly symmetric condition. Moreover, we obtain the first 5-approximation algorithm (4-approximation algorithm) for the MRPWCP (MCPCP) with the weakly symmetric condition. [ABSTRACT FROM AUTHOR]

In 1976–1977, Polyak published in the journal Avtomatica i Telemekhanika (Automation and Remote Control) two remarkable papers on how to study the properties of estimates of iterative pseudogradient algorithms. The first paper published in 1976 considered the general case based on the stochastic Lyapunov function, and the second one considered the linear case. The assumptions formulated in these papers and the estimates obtained in them can still be considered the state-of-the art. In the current paper, Polyak's approach is applied to the study of the properties of estimates of a (randomized) stochastic approximation search algorithm for the case of unknown-but-bounded noise in observations. The obtained asymptotic estimates were already known earlier, and exact estimates for a finite number of observations are published for the first time. [ABSTRACT FROM AUTHOR]

Quantum approximate optimization algorithms are hybrid quantum-classical variational algorithms designed to approximately solve combinatorial optimization problems such as the MAX-CUT problem. In spite of its potential for near-term quantum applications, it has been known that quantum approximate optimization algorithms have limitations for certain instances to solve the MAX-CUT problem, at any constant level p. Recently, the recursive quantum approximate optimization algorithm, which is a non-local version of quantum approximate optimization algorithm, has been proposed to overcome these limitations. However, it has been shown by mostly numerical evidences that the recursive quantum approximate optimization algorithm outperforms the original quantum approximate optimization algorithm for specific instances. In this paper, we analytically prove that the recursive quantum approximate optimization algorithm is more competitive than the original one to solve the MAX-CUT problem for complete graphs with respect to the approximation ratio. [ABSTRACT FROM AUTHOR]

We present approximation algorithms for several network design problems in the model of flexible graph connectivity (Adjiashvili et al., in: IPCO, pp 13–26, 2020, Math Program 1–33, 2021). Let k ≥ 1 , p ≥ 1 and q ≥ 0 be integers. In an instance of the (p, q)-Flexible Graph Connectivity problem, denoted (p , q) -FGC , we have an undirected connected graph G = (V , E) , a partition of E into a set of safe edges S and a set of unsafe edges U , and nonnegative costs c : E → R ≥ 0 on the edges. A subset F ⊆ E of edges is feasible for the (p , q) -FGC problem if for any set F ′ ⊆ U with | F ′ | ≤ q , the subgraph (V , F \ F ′) is p-edge connected. The algorithmic goal is to find a feasible solution F that minimizes c (F) = ∑ e ∈ F c e . We present a simple 2-approximation algorithm for the (1 , 1) -FGC problem via a reduction to the minimum-cost rooted 2-arborescence problem. This improves on the 2.527-approximation algorithm of Adjiashvili et al. Our 2-approximation algorithm for the (1 , 1) -FGC problem extends to a (k + 1) -approximation algorithm for the (1 , k) -FGC problem. We present a 4-approximation algorithm for the (k , 1) -FGC problem, and an O (q log | V |) -approximation algorithm for the (p , q) -FGC problem. Finally, we improve on the result of Adjiashvili et al. for the unweighted (1 , 1) -FGC problem by presenting a 16/11-approximation algorithm. The (p , q) -FGC problem is related to the well-known Capacitatedk-Connected Subgraph problem (denoted Cap- k -ECSS ) that arises in the area of Capacitated Network Design. We give a min (k , 2 u max) -approximation algorithm for the Cap- k -ECSS problem, where u max denotes the maximum capacity of an edge. [ABSTRACT FROM AUTHOR]

In the 70 s, Berge introduced 1-extendable graphs (also called B-graphs), which are graphs where every vertex belongs to a maximum independent set. Motivated by an application in the design of wireless networks, we study the computational complexity of 1-extendability, the problem of deciding whether a graph is 1-extendable. We show that, in general, 1-extendability cannot be solved in 2 o (n) time assuming the Exponential Time Hypothesis, where n is the number of vertices of the input graph, and that it remains NP-hard in subcubic planar graphs and in unit disk graphs (which is a natural model for wireless networks). Although 1-extendability seems to be very close to the problem of finding an independent set of maximum size (a.k.a.Maximum Independent Set), we show that, interestingly, there exist 1-extendable graphs for which Maximum Independent Set is NP-hard. Finally, we investigate a parameterized version of 1-extendability. [ABSTRACT FROM AUTHOR]

This paper constructs an interval partition linearization algorithm for solving minimax linear fractional programming (MLFP) problem. In this algorithm, MLFP is converted and decomposed into a series of linear programs by dividing the outer 1-dimensional space of the equivalent problem (EP) into polynomially countable intervals. To improve the computational efficiency of the algorithm, two new acceleration techniques are introduced, in which the regions in outer space where the optimal solution of EP does not exist are largely deleted. In addition, the global convergence of the proposed algorithm is summarized, and its computational complexity is illustrated to reveal that it is a fully polynomial time approximation scheme. Finally, the numerical results demonstrate that the proposed algorithm is feasible and effective. [ABSTRACT FROM AUTHOR]

This paper considers several two-machine open shop problems with two agents. Each agent has an independent set of nonpreemptive jobs, and the objective is to find either a schedule minimizing a linear combination of the makespans of both agents, a schedule minimizing the makespan of one agent with the makespan of the other agent not exceeding a threshold, or all Pareto-optimal schedules with respect to the makespans of both agents. We present a number of results for the problems above, including a polynomial algorithm and a pseudo-polynomial algorithm for special cases, non-approximability, two approximation algorithms, and a fully polynomial-time approximation scheme. Finally, we run numerical experiments to show the effectiveness of the pseudo-polynomial algorithm and the approximation algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we study the following robust optimization problem. Given a set family representing feasibility and candidate objective functions, we choose a feasible set, and then an adversary chooses one objective function, knowing our choice. The goal is to find a randomized strategy (i.e., a probability distribution over the feasible sets) that maximizes the expected objective value in the worst case. This problem is fundamental in wide areas such as artificial intelligence, machine learning, game theory, and optimization. To solve the problem, we provide a general framework based on the dual linear programming problem. In the framework, we utilize the ellipsoid algorithm with the approximate separation algorithm. We prove that there exists an α -approximation algorithm for our robust optimization problem if there exists an α -approximation algorithm for finding a (deterministic) feasible set that maximizes a nonnegative linear combination of the candidate objective functions. Using our result, we provide approximation algorithms for the max–min fair randomized allocation problem and the maximum cardinality robustness problem with a knapsack constraint. [ABSTRACT FROM AUTHOR]

In the general max–min fair allocation problem, there are m players and n indivisible resources, each player has his/her own utilities for the resources, and the goal is to find an assignment that maximizes the minimum total utility of resources assigned to a player. The problem finds many natural applications such as bandwidth distribution in telecom networks, processor allocation in computational grids, and even public-sector decision making. We introduce an over-estimation strategy to design approximation algorithms for this problem. When all utilities are positive, we obtain an approximation ratio of c 1 - ϵ , where c is the maximum ratio of the largest utility to the smallest utility of any resource. When some utilities are zero, we obtain an approximation ratio of (1 + 3 c ^ + O (δ c ^ 2)) , where c ^ is the maximum ratio of the largest utility to the smallest positive utility of any resource. [ABSTRACT FROM AUTHOR]

Several studies have reported methods for capturing ground reaction forces in the field. However, these forces are usually measured indirectly with non-interpretable "black box" models. Here we report an interpretable model with a function approximation algorithm. The model uses time series of plantar pressure from instrumented insoles to estimate vertical ground reaction forces. The study included data from 16 persons moving at different speeds on a two-belt treadmill equipped with force plates. The introduced regression model, based on a high-dimensional approximation, using only low-dimensional variable interactions, demonstrated its ability to estimate vertical ground reaction forces. The normalized mean square error for velocities between 3 and 9 km h - 1 ranged from 10.6 to 24.4 % . The accuracy of the presented approach, which can be used to analyze and interpret the learned model, was comparable to that reported in the literature. Furthermore, the evaluation of the learned model is particularly suitable for embedded and portable systems and, after a one-time calibration measurement, allows permanent and laboratory-independent measurement of vertical ground reaction forces. [ABSTRACT FROM AUTHOR]

Submodular maximization is a NP-hard combinatorial optimization problem regularly used in machine learning and data mining with large-scale data sets. To quantify the running time of approximation algorithms, the query complexity and adaptive complexity are two important measures, where the adaptivity of an algorithm is the number of sequential rounds it makes when each round can execute polynomially many function evaluations in parallel. These two concepts reasonably quantify the efficiency and practicability of parallel computation. In this paper, we consider the problem of maximizing a nonnegative monotone DR-submodular function over a bounded integer lattice with a cardinality constraint in a value oracle model. Prior to our work, Soma and Yoshida (Math Program 172:539–563, 2018) have studied this problem and present an approximation algorithm with almost optimal approximate ratio and the same adaptivity and query complexity. We develop two novel algorithms, called low query algorithm and low adaptivity algorithm, which have approximation ratios equal to Soma and Yoshida (2018), but reach a new record of query complexity and adaptivity. As for methods, compared with the threshold greedy in Soma and Yoshida (2018), the low query algorithm reduces the number of possible thresholds and improves both the adaptivity and query complexity. The low adaptivity algorithm further integrates a vector sequencing technique to accelerate adaptive complexity in an exponential manner while only making logarithmic sacrifices on oracle queries. [ABSTRACT FROM AUTHOR]

This paper introduces the d-distanceb-matching problem, in which we are given a bipartite graph G = (S , T ; E) with S = { s 1 , ⋯ , s n } , a weight function on the edges, an integer d ∈ Z + and a degree bound function b : S ∪ T → Z + . The goal is to find a maximum-weight subset M ⊆ E of the edges satisfying the following two conditions: (1) the degree of each node v ∈ S ∪ T is at most b(v) in M, (2) if s i t , s j t ∈ M , then | i - j | ≥ d . In the cyclic version of the problem, the nodes in S are considered to be in cyclic order. We get back the (cyclic)d-distance matching problem when b (s) = 1 for s ∈ S and b (t) = ∞ for t ∈ T . We prove that the d-distance matching problem is APX-hard, even in the unweighted case. We show that 2 - 1 d is a tight upper bound on the integrality gap of the natural integer programming model for the cyclic d-distance b-matching problem provided that (2 d - 1) divides the size of S. For the non-cyclic case, the integrality gap is shown to be at most (2 - 2 d) . The proofs give approximation algorithms with guarantees matching these bounds, and also improve the best known algorithms for the (cyclic) d-distance matching problem. In a related problem, our goal is to find a permutation of S maximizing the weight of the optimal d-distance b-matching. This problem can be solved in polynomial time for the (cyclic) d-distance matching problem — even though the (cyclic) d-distance matching problem itself is NP-hard and also hard to approximate arbitrarily. For (cyclic) d-distance b-matchings, however, we prove that finding the best permutation is NP-hard, even if b ≡ 2 or d = 2 , and we give e-approximation algorithms. [ABSTRACT FROM AUTHOR]

This study addresses the energy efficiency challenge in cloud data centers by examining the Virtual Machine Placement (VMP) problem. VMP involves mapping virtual machines (VMs) to physical machines (PMs) under capacity constraints. The paper focuses on the bin packing with linear usage cost (BPLUC) variant of bin packing, which includes fixed and variable costs in the calculation of the cost of a used bin. We prove that every approximation algorithm for the bin and vector bin packing can be used for BPLUC and VBPLUC, respectively. We propose a more power-efficient approach to VMP by applying a vector bin packing algorithm to minimize power consumption in data centers. We test the proposed algorithm on various synthetic and real workloads, and the experimental results demonstrate that it is more power-efficient than existing algorithms for VMP. The findings suggest that the proposed algorithm has significant implications for energy-efficient strategies in cloud data centers. Generally, this study makes contributes to the development of energy-efficient approaches to VMP that can help reduce power consumption and improve the sustainability of cloud data centers. [ABSTRACT FROM AUTHOR]

We initiate the work on maximin share (MMS) fair allocation of m indivisible chores to n agents using only their ordinal preferences, from both algorithmic and mechanism design perspectives. The previous best-known approximation ratio using ordinal preferences is 2 - 1 / n by Aziz et al. [AAAI 2017]. We improve this result by giving a deterministic 5/3-approximation algorithm that determines an allocation sequence of agents, according to which items are allocated one by one. By a tighter analysis, we show that for n = 2 and 3, our algorithm achieves better approximation ratios, and is actually optimal. We also consider the setting with strategic agents, where agents may misreport their preferences to manipulate the outcome. We first provide a strategyproof O (log (m / n)) -approximation consecutive picking algorithm, and then improve the approximation ratio to O (log n) by a randomized algorithm. Both algorithms only use the ordinal preferences of agents. Our results uncover some interesting contrasts between the approximation ratios achieved for chores versus goods. [ABSTRACT FROM AUTHOR]

We consider the robust version of the classic k-center clustering problem, where we wish to remove up to z points (outliers), so as to be able to cluster the remaining points in k clusters with minimum maximum radius. We study such a problem under the fully dynamic adversarial model, where points can be inserted or deleted arbitrarily. In this setting, the main goal is to design algorithms that maintain a high quality solution at any point in time, while requiring a "small" amortized cost, i.e. a "small" number of operations per insertion or deletion, on average. In our work, we provide the first constant bi-criteria approximation algorithm for such a problem with its amortized cost being independent of both z and the size of the current input. We also complement our positive result with a lower bound showing that any constant (non bi-criteria) approximation algorithm has amortized cost at least linear in z. Finally, we conduct an in-depth experimental analysis of our algorithm on Twitter, Flickr, and Air-Quality datasets showing the effectiveness of our approach. [ABSTRACT FROM AUTHOR]

We prove that Simulated Annealing with an appropriate cooling schedule computes arbitrarily tight constant-factor approximations to the minimum spanning tree problem in polynomial time. This result was conjectured by Wegener (Automata, Languages and Programming, ICALP, Berlin, 2005). More precisely, denoting by n , m , w max , and w min the number of vertices and edges as well as the maximum and minimum edge weight of the MST instance, we prove that simulated annealing with initial temperature T 0 ≥ w max and multiplicative cooling schedule with factor 1 - 1 / ℓ , where ℓ = ω (m n ln (m)) , with probability at least 1 - 1 / m computes in time O (ℓ (ln ln (ℓ) + ln (T 0 / w min))) a spanning tree with weight at most 1 + κ times the optimum weight, where 1 + κ = (1 + o (1)) ln (ℓ m) ln (ℓ) - ln (m n ln (m)) . Consequently, for any ϵ > 0 , we can choose ℓ in such a way that a (1 + ϵ) -approximation is found in time O ((m n ln (n)) 1 + 1 / ϵ + o (1) (ln ln n + ln (T 0 / w min))) with probability at least 1 - 1 / m . In the special case of so-called (1 + ϵ) -separated weights, this algorithm computes an optimal solution (again in time O ((m n ln (n)) 1 + 1 / ϵ + o (1) (ln ln n + ln (T 0 / w min))) ), which is a significant speed-up over Wegener's runtime guarantee of O (m 8 + 8 / ϵ) . Our tighter upper bound also admits the result that in some situations a hybridization of simulated annealing and the (1 + 1) EA can lead to stronger runtime guarantees than either algorithm alone. [ABSTRACT FROM AUTHOR]

An algorithm for automatic approximation of the time dependence x(t) is built for the observed coordinate of the coronal mass ejection (CME) front from the admissible starting point to the first appearance in the field of view of the LASCO coronagraph and further, up to a heliocentric distance of ~25 solar radii (RS). In the region from the starting point to the first appearance of the CME, two sections are assumed, with uniform (impulsive) acceleration and with uniform motion; then, the motion is approximated by observations. At the beginning of the approximation, either the CME start time is found through the appearance of certain frequencies of radio emissions (RSTN data) and type II and IV radio emissions (sequence characteristics are determined by machine learning), or the start time is determined by averaging over the allowable takeoff area; then the polynomial-ballistic model is optimized. The first and second derivatives x(t) determine the speed and acceleration of the CME at any point of its trajectory. Such an algorithm is necessary to obtain the most accurate kinematic characteristics of CMEs, which can allow one to study the physical, spatial, and temporal relationships between flares and CMEs in all their diversity. Widely used approximation techniques simplify the real CME trajectories x(t), thereby possibly discarding important features of the CME kinematics and flare development in the posteruptive phase. The algorithm was trained and tested on 17 solar flares and associated CMEs, which are known for their powerful proton events with proton energies greater than 300 MeV. The rate of the first occurrence of CMEs turned out to be different from the average rate given in the LASCO catalog, which is important for estimating the energy of flares and CMEs. In 7 out of 17 events, there was acceleration only in the impulsive phase (and then deceleration), while acceleration in the impulsive and posteruptive phases occurred in 10 events. In 4 out of 17 events, CME velocities greater than 2000 km/s were reached at a distance of 20RS. The accuracy of determining the kinematic characteristics of CMEs can be improved by using additional observations, for example, SDO AIA in the September 10, 2017 event. [ABSTRACT FROM AUTHOR]

We introduce a dynamical system to the problem of finding zeros of the sum of two maximally monotone operators. We investigate the existence, uniqueness and extendability of solutions to this dynamical system in a Hilbert space. We prove that the trajectories of the proposed dynamical system converge strongly to a primal–dual solution of the considered problem. Under explicit time discretization of the dynamical system we obtain the best approximation algorithm for solving coupled monotone inclusion problem. [ABSTRACT FROM AUTHOR]

In this paper, the first fixed-ratio approximation algorithms are proposed for a series of asymmetric settings of well-known combinatorial routing problems. Among them are the Steiner cycle problem, the prize-collecting traveling salesman problem, the minimum cost cycle cover problem by a bounded number of cycles, etc. Almost all of the proposed algorithms rely on original reductions of the considered problems to auxiliary instances of the asymmetric traveling salesman problem and employ the breakthrough approximation results for this problem obtained recently by O. Svensson, J. Tarnawski, L. Végh, V. Traub, and J. Vygen. On the other hand, approximation of the cycle cover problem was proved by applying a deeper extension of their approach. [ABSTRACT FROM AUTHOR]

We devise the first constant-factor approximation algorithm for finding an integral multi-commodity flow of maximum total value for instances where the supply graph together with the demand edges can be embedded on an orientable surface of bounded genus. This extends recent results for planar instances. Our techniques include an uncrossing algorithm, which is significantly more difficult than in the planar case, a partition of the cycles in the support of an LP solution into free homotopy classes, and a new rounding procedure for freely homotopic non-separating cycles. [ABSTRACT FROM AUTHOR]

The gate-based model is one of the leading quantum computing paradigms for representing quantum circuits. Within this paradigm, a quantum algorithm is expressed in terms of a set of quantum gates that are executed on the quantum hardware over time, subject to a number of constraints whose satisfaction must be guaranteed before running the circuit, to allow for feasible execution. The need to guarantee the previous feasibility condition gives rise to the Quantum Circuit Compilation Problem (QCCP). The QCCP has been demonstrated to be NP-Complete, and can be considered as a Planning and Scheduling problem. In this paper, we consider quantum compilation instances deriving from the general Quantum Approximation Optimization Algorithm (QAOA), applied to the MaxCut problem, devised to be executed on Noisy Intermediate Scale Quantum (NISQ) hardware architectures. More specifically, in addition to the basic QCCP version, we also tackle other variants of the same problem such as the QCCP-X (QCCP with crosstalk constraints), the QCCP-V (QCCP with variable qubit state initialization), as well as the QCCP-VX that includes both previous variants. All problem variants are solved using genetic algorithms. We perform an experimental study across a conventional set of instances taken from the literature, and show that the proposed genetic algorithm, termed G A VX , outperforms previous approaches in the literature. [ABSTRACT FROM AUTHOR]

Simple heuristics for (combinatorial) optimization problems often show a remarkable performance in practice. Worst-case analysis often falls short of explaining this performance. Because of this, "beyond worst-case analysis" of algorithms has recently gained a lot of attention, including probabilistic analysis of algorithms. The instances of many (combinatorial) optimization problems are essentially a discrete metric space. Probabilistic analysis for such metric optimization problems has nevertheless mostly been conducted on instances drawn from Euclidean space, which provides a structure that is usually heavily exploited in the analysis. However, most instances from practice are not Euclidean. Little work has been done on metric instances drawn from other, more realistic, distributions. Some initial results have been obtained in recent years, where random shortest path metrics generated from dense graphs (either complete graphs or Erdős–Rényi random graphs) have been used so far. In this paper we extend these findings to sparse graphs, with a focus on sparse graphs with 'fast growing cut sizes', i.e. graphs for which | δ (U) | = Ω (| U | ε) for some constant ε ∈ (0 , 1) for all subsets U of the vertices, where δ (U) is the set of edges connecting U to the remaining vertices. A random shortest path metric is constructed by drawing independent random edge weights for each edge in the graph and setting the distance between every pair of vertices to the length of a shortest path between them with respect to the drawn weights. For such instances generated from a sparse graph with fast growing cut sizes, we prove that the greedy heuristic for the minimum distance maximum matching problem, and the nearest neighbor and insertion heuristics for the traveling salesman problem all achieve a constant expected approximation ratio. Additionally, for instances generated from an arbitrary sparse graph, we show that the 2-opt heuristic for the traveling salesman problem also achieves a constant expected approximation ratio. [ABSTRACT FROM AUTHOR]

We study the Non-preemptive Peak Demand Minimization (NPDM) problem, where we are given a set of jobs, specified by their processing times and energy requirements. The goal is to schedule all jobs within a fixed time period such that the peak load (the maximum total energy requirement at any time) is minimized. This problem has recently received significant attention due to its relevance in smart-grids. Theoretically, the problem is related to the classical strip packing problem (SP). In SP, a given set of axis-aligned rectangles must be packed into a fixed-width strip, such that the height of the strip is minimized. NPDM can be modeled as strip packing with slicing and stacking constraint: each rectangle may be cut vertically into multiple slices and the slices may be packed into the strip as individual pieces. The stacking constraint forbids solutions where two slices of the same rectangle are intersected by the same vertical line. Non-preemption enforces the slices to be placed in contiguous horizontal locations (but may be placed at different vertical locations). We obtain a (5 / 3 + ε) -approximation algorithm for the problem. We also provide an asymptotic efficient polynomial-time approximation scheme (AEPTAS) which generates a schedule for almost all jobs with energy consumption (1 + ε) OPT . The remaining jobs fit into a thin container of height 1. This AEPTAS is used as a subroutine to acquire the (5 / 3 + ε) -approximation algorithm. The previous best result for NPDM was a 2.7-approximation based on FFDH (Ranjan et al., in: 2015 IEEE symposium on computers and communication (ISCC), pp 758–763, IEEE, 2015). One of our key ideas is providing several new lower bounds on the optimal solution of a geometric packing, which could be useful in other related problems. These lower bounds help us to obtain approximative solutions based on Steinberg's algorithm in many cases. In addition, we show how to split schedules generated by the AEPTAS into few segments and to rearrange the corresponding jobs to insert the thin container mentioned above, such that it does not exceed the bound of (5 / 3 + ε) OPT . [ABSTRACT FROM AUTHOR]

We present deterministic algorithms for maintaining a (3 / 2 + ϵ) and (2 + ϵ) -approximate maximum matching in a fully dynamic graph with worst-case update times O ^ (n) and O ~ (1) respectively. The fastest known deterministic worst-case update time algorithms for achieving approximation ratio (2 - δ) (for any δ > 0 ) and (2 + ϵ) were both shown by Roghani et al. (Beating the folklore algorithm for dynamic matching, 2021) with update times O (n 3 / 4) and O ϵ (n) respectively. We close the gap between worst-case and amortized algorithms for the two approximation ratios as the best deterministic amortized update times for the problem are O ϵ (n) and O ~ (1) which were shown in Bernstein and Stein (in: Proceedings of the twenty-seventh annual ACM-SIAM symposium on discrete algorithms, 2016) and Bhattacharya and Kiss (in: 48th international colloquium on automata, languages, and programming, ICALP 2021, 12–16 July, Glasgow, 2021) respectively. The algorithm achieving (3 / 2 + ϵ) approximation builds on the EDCS concept introduced by the influential paper of Bernstein and Stein (in: International colloquium on automata, languages, and programming, Springer, Berlin, 2015). Say that H is a (α , δ) -approximate matching sparsifier if at all times H satisfies that μ (H) · α + δ · n ≥ μ (G) (define (α , δ) -approximation similarly for matchings). We show how to maintain a locally damaged version of the EDCS which is a (3 / 2 + ϵ , δ) -approximate matching sparsifier. We further show how to reduce the maintenance of an α -approximate maximum matching to the maintenance of an (α , δ) -approximate maximum matching building based on an observation of Assadi et al. (in: Proceedings of the twenty-seventh annual (ACM-SIAM) symposium on discrete algorithms, (SODA) 2016, Arlington, VA, USA, January 10–12, 2016). Our reduction requires an update time blow-up of O ^ (1) or O ~ (1) and is deterministic or randomized against an adaptive adversary respectively. To achieve (2 + ϵ) -approximation we improve on the update time guarantee of an algorithm of Bhattacharya and Kiss (in: 48th International colloquium on automata, languages, and programming, ICALP 2021, 12–16 July, Glasgow, 2021). In order to achieve both results we explicitly state a method implicitly used in Nanongkai and Saranurak (in: Proceedings of the twenty-seventh annual ACM symposium on theory of computing, 2017) and Bernstein et al. (Fully-dynamic graph sparsifiers against an adaptive adversary, 2020) which allows to transform dynamic algorithms capable of processing the input in batches to a dynamic algorithms with worst-case update time. [ABSTRACT FROM AUTHOR]

The minimum weighted vertex cover (MWVC) problem is to find a subset of vertices that can cover all the edges of the network and minimize the sum of the vertex weights in the vertex subset. MWVC is a generalization of the minimum vertex cover (MVC) problem and can be regarded as a combinatorial optimization problem. This paper proposes an evolutionary algorithm based on the snowdrift game to solve the MWVC problem. We use the evolutionary algorithm framework, and the snowdrift game is combined to construct and improve the initial solution. First, the network's vertex is regarded as an intelligent agent, and each vertex and its neighbors play a snowdrift game to form an initial solution. Then local search and global search are used to improve the initial solution. The solution is improved according to the proposed score function in the local search stage to obtain a better MWVC solution. The evolutionary algorithm is used in the global search stage to escape the local optimum. Experiments on different networks show that the proposed algorithm are effective on weighted networks. [ABSTRACT FROM AUTHOR]

We investigate the optimal piecewise linear interpolation of the bivariate product xy over rectangular domains. More precisely, our aim is to minimize the number of simplices in the triangulation underlying the interpolation, while respecting a prescribed approximation error. First, we show how to construct optimal triangulations consisting of up to five simplices. Using these as building blocks, we construct a triangulation scheme called crossing swords that requires at most - times the number of simplices in any optimal triangulation. In other words, we derive an approximation algorithm for the optimal triangulation problem. We also show that crossing swords yields optimal triangulations in the case that each simplex has at least one axis-parallel edge. Furthermore, we present approximation guarantees for other well-known triangulation schemes, namely for the red refinement and longest-edge bisection strategies as well as for a generalized version of K1-triangulations. Thereby, we are able to show that our novel approach dominates previous triangulation schemes from the literature, which is underlined by illustrative numerical examples. [ABSTRACT FROM AUTHOR]

For a graph G = (V , E) , a collection P of vertex-disjoint (simple) paths is called a path cover of G if every vertex v ∈ V is contained in exactly one path of P . The Path Cover problem (PC for short) is to find a minimum cardinality path cover of G. In this paper, we introduce generalizations of PC, where each path is associated with a weight (cost or profit). Our problem, Minimum (Maximum) Weighted Path Cover [MinPC (MaxPC)], is defined as follows: Let U = { 0 , 1 , ⋯ , n - 1 } . Given a graph G = (V , E) and a weight function f : U → R ∪ { + ∞ , - ∞ } that defines a weight for each path based on its length, the objective of MinPC (MaxPC) is to find a path cover P of G such that the total weight of the paths in P is minimized (maximized). Let L be a subset of U, and P L be the set of paths such that each path is of length ℓ ∈ L . We consider Min P L PC with binary cost, i.e., the cost function is f (ℓ) = 1 if ℓ ∈ L ; otherwise, f (ℓ) = 0 . We also consider Max P L PC with f (ℓ) = ℓ + 1 , if ℓ ∈ L ; otherwise, f (ℓ) = 0 . Many well-known graph theoretic problems such as the Hamiltonian Path and the Maximum Matching problems can be modeled using Min P L PC and Max P L PC. In this paper, we first show that deciding whether Min P { 0 , 1 , 2 } PC has a 0-weight solution is NP-complete for planar bipartite graphs of maximum degree three, and consequently, (i) for any constant σ ≥ 1 , there is no polynomial-time approximation algorithm with approximation ratio σ for Min P { 0 , 1 , 2 } PC unless P = NP, and (ii) Max P { 3 , ⋯ , n - 1 } PC is NP-hard for the same graph class. Next, we present a polynomial-time algorithm for Min P { 0 , 1 , ⋯ , k } PC on graphs with bounded treewidth for a fixed k. Lastly, we present a 4-approximation algorithm for Max P { 3 , ⋯ , n - 1 } PC, which becomes a 2.5-approximation algorithm for subcubic graphs. [ABSTRACT FROM AUTHOR]

We present a number of complexity results concerning the problem of counting vertices of an integral polytope defined by a system of linear inequalities. The focus is on polytopes with small integer vertices, particularly 0/1 polytopes and half-integral polytopes. [ABSTRACT FROM AUTHOR]

A graph is called a sum graph if its vertices can be labelled by distinct positive integers such that there is an edge between two vertices if and only if the sum of their labels is the label of another vertex of the graph. Most papers on sum graphs consider combinatorial questions like the minimum number of isolated vertices that need to be added to a given graph to make it a sum graph. In this paper, we initiate the study of sum graphs from the viewpoint of computational complexity. Notice that every n-vertex sum graph can be represented by a sorted list of n positive integers where edge queries can be answered in O (log n) time. Therefore, upper-bounding the numbers used as vertex labels also upper-bounds the space complexity of storing the graph in the database. We show that every n-vertex, m-edge, d-degenerate graph can be made a sum graph by adding at most m isolated vertices to it, such that the largest numbers used as vertex labels grows as O (n 2 d) . This enables us to store the graph using O (m log n) bits of memory. For sparse graphs (graphs with O (n) edges), this matches the trivial lower bound of Ω (n log n) . As planar graphs and forests have constant degeneracy, our result implies an upper bound of O (n 2) on their label numbers. The previously best known upper bound on the numbers needed for labelling general graphs with the minimum number of isolated vertices was O (4 n) , due to Kratochvíl, Miller & Nguyen (2001). Furthermore, their proof was existential, whereas our labelling can be constructed in polynomial time. [ABSTRACT FROM AUTHOR]

In the Strip Packing problem, we are given a vertical half-strip [ 0 , W ] × [ 0 , + ∞) and a collection of open rectangles of width at most W. Our goal is to find an axis-aligned (non-overlapping) packing of such rectangles into the strip such that the maximum height OPT spanned by the packing is as small as possible. It is NP-hard to approximate this problem within a factor (3 / 2 - ε) for any constant ε > 0 by a simple reduction from the Partition problem, while the current best approximation factor for it is (5 / 3 + ε) . It seems plausible that Strip Packing admits a (3 / 2 + ε) -approximation. We make progress in that direction by achieving such tight approximation guarantees for a special family of instances, which we call skewed instances. As standard in the area, for a given constant parameter δ > 0 , we call large the rectangles with width at least δ W and height at least δ O P T , and skewed the remaining rectangles. If all the rectangles in the input are large, then one can easily compute the optimal packing in polynomial time (since the input can contain only a constant number of rectangles). We consider the complementary case where all the rectangles are skewed. This second case retains a large part of the complexity of the original problem; in particular, the skewed case is still NP-hard to approximate within a factor (3 / 2 - ε) , and we provide an (almost) tight (3 / 2 + ε) -approximation algorithm. [ABSTRACT FROM AUTHOR]

This paper presents a combined method for the equivalent circuit parameters estimation of cage induction motors. The method is based on dual usage of the particle swarm optimization algorithm and the approximation of rotor parameters as a function of the speed, due to the influence of the skin effect. The approximation of rotor parameters as a function of the speed is not directly applied in the parameters estimation algorithm, but it is used to obtain the torque-speed characteristics of cage induction motors. The first stage of the optimization includes the estimation of equivalent circuit parameters of a motor for the nominal operating mode, while the rotor parameters at the start of the motor are estimated in the second stage of the optimization. These parameters are obtained as a result of minimizing the error between the calculated and the manufacture data. The proposed method is applied on eight two-pole induction motors with different rated powers, energy efficiency class IE3, manufactured by ABB. The results are verified by comparing the obtained torque-speed characteristics with the corresponding characteristics provided by the manufacturer (i.e., ABB) using the MotSize program. It is shown that the torque-speed characteristics obtained by the proposed method are in a good agreement with the characteristics given by the manufacturer. Also, the value of the mean absolute relative error does not exceed 5% for all considered motors. [ABSTRACT FROM AUTHOR]

In this paper we consider the coupled task scheduling problem with exact delay times on a single machine with the objective of minimizing the total completion time of the jobs. We provide constant-factor approximation algorithms for several variants of this problem that are known to be N P -hard, while also proving N P -hardness for two variants whose complexity was unknown before. Using these results, together with constant-factor approximations for the makespan objective from the literature, we also introduce the first results on bi-objective approximation in the coupled task setting. [ABSTRACT FROM AUTHOR]

Based on results of experiments, we analyze the efficiency of some exact and approximation algorithms for a semi-supervised graph 2-clustering problem. [ABSTRACT FROM AUTHOR]

In this paper, we give an algorithm that finds an ϵ -approximate solution to a mixed integer quadratic programming (MIQP) problem. The algorithm runs in polynomial time if the rank of the quadratic function and the number of integer variables are fixed. The running time of the algorithm is expected unless P = NP. In order to design this algorithm we introduce the novel concepts of spherical form MIQP and of aligned vectors, and we provide a number of results of independent interest. In particular, we give a strongly polynomial algorithm to find a symmetric decomposition of a matrix, and show a related result on simultaneous diagonalization of matrices. [ABSTRACT FROM AUTHOR]

We study algorithmic Bayesian persuasion problems in which the principal (a.k.a. the sender) has to persuade multiple agents (a.k.a. receivers) by using public communication channels. Specifically, our model follows the multi-receiver model with no inter-agent externalities introduced by Arieli and Babichenko (J Econ Theory 182:185–217, 2019). It is known that the problem of computing a sender-optimal public persuasive signaling scheme is not approximable even in simple settings. Therefore, prior works usually focus on determining restricted classes of the problem for which efficient approximation is possible. Typically, positive results in this space amounts to finding bi-criteria approximation algorithms yielding an almost optimal and almost persuasive solution in polynomial time. In this paper, we take a different perspective and study the persuasion problem in the general setting where the space of the states of nature, the action space of the receivers, and the utility function of the sender can be arbitrary. We fully characterize the computational complexity of computing a bi-criteria approximation of an optimal public signaling scheme in such settings. In particular, we show that, assuming the Exponential Time Hypothesis, solving this problem requires at least a quasi-polynomial number of steps even in instances with simple utility functions and binary action spaces such as an election with the k-voting rule. In doing so, we prove that a relaxed version of the Maximum Feasible Subsystem of Linear Inequalities problem requires at least quasi-polynomial time to be solved. Finally, we close the gap by providing a quasi-polynomial time bi-criteria approximation algorithm for arbitrary public persuasion problems that, under mild assumptions, yields a QPTAS. [ABSTRACT FROM AUTHOR]

In Two-dimensional Bin Packing (2BP), we are given n rectangles as input and our goal is to find an axis-aligned nonoverlapping packing of these rectangles into the minimum number of unit square bins. 2BP admits no APTAS and the current best approximation ratio is 1.406 by Bansal and Khan (ACM-SIAM symposium on discrete algorithms (SODA), pp 13–25, 2014. https://doi.org/10.1137/1.9781611973402.2). A well-studied variant of 2BP is Guillotine Two-dimensional Bin Packing (G2BP), where rectangles must be packed in such a way that every rectangle in the packing can be obtained by applying a sequence of end-to-end axis-parallel cuts, also called guillotine cuts. Bansal et al. (Symposium on foundations of computer science (FOCS). IEEE, pp 657–666, 2005. https://doi.org/10.1109/SFCS.2005.10) gave an APTAS for G2BP. Let λ be the smallest constant such that for every set I of items, the number of bins in the optimal solution to G2BP for I is upper bounded by λ opt (I) + c , where opt (I) is the number of bins in the optimal solution to 2BP for I and c is a constant. It is known that 4 / 3 ≤ λ ≤ 1.692 . Bansal and Khan (2014) conjectured that λ = 4 / 3 . The conjecture, if true, will imply a (4 / 3 + ε) -approximation algorithm for 2BP. Given a small constant δ > 0 , a rectangle is called large if both its height and width are at least δ , else it is called skewed. We make progress towards the conjecture by showing that λ = 4 / 3 when all input rectangles are skewed. We also give an APTAS for 2BP for skewed items, though general 2BP does not admit an APTAS. [ABSTRACT FROM AUTHOR]

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]

Feature selection is an essential task in the field of machine learning, data mining, and pattern recognition, primarily, when we deal with a large number of features. Feature selection assists in enhancing prediction accuracy, reducing computation time, and creating more comprehensible models. In feature selection, each feature has two possibilities, either it would be taken for computation or not, which implies for n number of features, there are 2 n possible feature subsets. So, identifying a relevant feature subset in a reasonable amount of time is an NP-hard problem, but by using an approximation algorithm, a near-optimal solution can be achieved. However, many of the feature selection algorithms use a sequential search strategy to select relevant features, which adds or removes features from the dataset sequentially and leads to trapped into a local optimum solution. In this paper, we propose a novel clustering-based hybrid feature selection approach using ant colony optimization that selects features randomly and measures the qualities of features by K-means clustering in terms of silhouette index and Laplacian score. The proposed feature selection approach allows random selection of features, which allows a better exploration of feature space and thus avoids the problem of being trapped in a local optimal solution, and generates a global optimal solution. The same is verified when compared with another state-of-the-art method. [ABSTRACT FROM AUTHOR]

In wireless sensor networks (WSNs), the virtual backbone (VB) consists of a subset of nodes, which are responsible for routing tasks. Fault-tolerant VBs are desirable for overcoming the effects of node or link failure in WSNs. Usually, a homogeneous WSN (VB) is abstracted as a unit disk graph (UDG) (connected dominating set(CDS)). This paper introduces the concept of a fault-tolerant CDS in a UDG called a ((2, 2), m)-CDS, which is different from a traditional fault-tolerant CDS ((k, m)-CDS). A ((2, 2), m)-CDS can still function even if one edge or one node fails, which implies that it possesses fault-tolerant properties for both nodes and edges, in contrast to traditional (k, m)-CDSs, which possess fault tolerance only for nodes. Then, we propose a 5 α -approximation algorithm for computing a ((2, 2), m)-CDS, where α is the performance ratio for computing a (2, m) -CDS, and analyze its time complexity. In simulations, we compare our algorithm with an existing algorithm for fault-tolerant CDS construction based on CDS size. From the simulations, we find that our algorithm outperforms its competitor in constructing a quality VB. [ABSTRACT FROM AUTHOR]

We study geometric variations of the discriminating code problem. In the discrete version of the problem, a finite set of points P and a finite set of objects S are given in R d . The objective is to choose a subset S ∗ ⊆ S of minimum cardinality such that for each point p i ∈ P , the subset S i ∗ ⊆ S ∗ covering p i satisfies S i ∗ ≠ ∅ , and each pair p i , p j ∈ P , i ≠ j , we have S i ∗ ≠ S j ∗ . In the continuous version of the problem, the solution set S ∗ can be chosen freely among a (potentially infinite) class of allowed geometric objects. In the 1-dimensional case ( d = 1 ), the points in P are placed on a horizontal line L, and the objects in S are finite-length line segments aligned with L (called intervals). We show that the discrete version of this problem is NP-complete. This is somewhat surprising as the continuous version is known to be polynomial-time solvable. This is also in contrast with most geometric covering problems, which are usually polynomial-time solvable in one dimension. Still for the 1-dimensional discrete version, we design a polynomial-time 2-approximation algorithm. We also design a PTAS for both discrete and continuous versions in one dimension, for the restriction where the intervals are all required to have the same length. We then study the 2-dimensional case ( d = 2 ) for axis-parallel unit square objects. We show that both continuous and discrete versions are NP-complete, and design polynomial-time approximation algorithms that produce (16 · O P T + 1) -approximate and (64 · O P T + 1) -approximate solutions respectively, using rounding of suitably defined integer linear programming problems. Finally, we apply our techniques to a related variant of the discrete problem, where instead of points and geometric objects we just have a set S of objects. The goal is to select a small subset S ∗ of objects so that all objects of S are discriminated by their intersection with the objects of S ∗ . This problem can be viewed as a graph problem by stating it in terms of the vertices of the geometric intersection graph of S. Under this graph-theoretical form, it is known as the identifying code problem. We show that the identifying code problem for axis-parallel unit square intersection graphs (in d = 2 ) can be solved in the same manner as for the discrete version of the discriminating code problem for unit square objects described above, and all our positive approximation results still hold in this setting. [ABSTRACT FROM AUTHOR]