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An improved algorithm for a two-stage production scheduling problem with an outsourcing option

THEORETICAL COMPUTER SCIENCE 2021年 876卷 59-69页

作者： Jiang, Xiaojuan Zhang, An Chen, Yong Chen, Guangting Lee, Kangbok Pohang Univ Sci & Technol Dept Ind & Management Engn Pohang 37673 South Korea Hangzhou Dianzi Univ Dept Math Hangzhou 310018 Peoples R China Taizhou Univ Taizhou 317000 Peoples R China

We consider a two-stage production scheduling problem where each operation can be outsourced or processed in-house. For each operation in the same machine, the ratio of its outsourcing cost to its processing time is constant. The objective is to minimize the sum of the makespan and the total outsourcing cost. It is known that this problem is either polynomial time solvable or NP-hard according to the conditions of the ratios. Even though approximation algorithms for NP-hard cases had been developed, their tight worst-case performance ratios are still open. In this paper, we carefully analyze the approximation algorithms to identify their tight worst-case performance ratios for cases. In one case, we propose a new approximation algorithm with a better and tight worst-case performance ratio. In the process of analyzing the algorithm, we propose a technique utilizing nonlinear optimization. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Scheduling Flow shop Outsourcing approximation algorithm Worst-case analysis

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Regularization-Based Coflow Scheduling in Optical Circuit Switches

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IEEE-ACM TRANSACTIONS ON NETWORKING 2021年第3期29卷 1280-1293页

作者： Tan, Haisheng Zhang, Chi Xu, Chao Li, Yupeng Han, Zhenhua Li, Xiang-Yang Univ Sci & Technol China USTC LINKE Lab Hefei 230052 Peoples R China Univ Sci & Technol China USTC CAS Key Lab Wireless Opt Commun Hefei 230052 Peoples R China Hong Kong Baptist Univ Dept Journalism Hong Kong Peoples R China Mircosoft Res Asia Shanghai 200232 Peoples R China

To improve the application-level data efficiency, the scheduling of coflows, defined as a collection of parallel flows sharing the same objective, is prevailing in recent data centers. Meanwhile, optical circuit switches (OCS) are gradually applied to provide high data rate with low power consumption. However, so far few research outputs have covered the flow, let alone the coflow, scheduling in the context of OCS. In this work, we investigate coflow scheduling in OCS-based data centers. We first derive a novel operation called regularization processed respectively on the flow traffic demands and the flow start times, which can be efficiently implemented and reduce the circuit reconfiguration frequency dramatically. We then propose a 2-approximation algorithm, called Reco-Sin, for single coflow scheduling to minimize the coflow completion time (CCT). For multiple coflows, we derive Reco-Mul to minimize the total weighted CCT, which can transform any non-preemptive multi-coflow scheduling in packet switches to a scheduling scheme in OCS. Reco-Mul can achieve a constant approximation under the assumption that no tiny flows will be transmitted in OCS. To get rid of this assumption, we present another multiple coflow scheduling scheme, named Reco-Mul+, which has an approximation ratio of O(K). Here, K is the total number of coflows. Extensive simulations based on Facebook data traces show that our approaches outperform state-of-the-art schemes significantly, i.e., one single coflow can be finished up to 1.97x faster with Reco-Sin, and multiple coflows can be completed up to more than 2x faster with Reco-Mul and Reco-Mul+.

关键词： Coflow Scheduling Optical Circuit Switch approximation algorithm

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Toward Efficient City-Scale Patrol Planning Using Decomposition and Grafting

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IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2021年第2期22卷 747-757页

作者： Wang, Wanyuan Dong, Zichen An, Bo Jiang, Yichuan Southeast Univ Lab Intelligent Syst & Social Comp Nanjing 211189 Peoples R China Southeast Univ Sch Comp Sci & Engn Nanjing 211189 Peoples R China Nanyang Technol Univ Sch Comp Sci & Engn Singapore 639798 Singapore

Motivated by the increasing need of the real-world patrolling, this paper studies a practical city-scale patrolling (CSP) variant. In CSP, the police are scheduled to patrol city regions, and the objective is not only to protect public security but also to respond to incidents timely. We use an integer program (IP) to formulate the CSP problem, with the objective of maximizing the police visibility rate (PVR) to improve public safety and the additional constraint of response time guarantee to handle incidents timely. For such an NP-hard problem, existing studies either cannot scale-up or do not provide a bound from optimum. To fill the research gap, we propose a decomposition and grafting approach. We first decompose the original CSP into two weakly-coupled subproblems, minimizing police problem (MinP) and maximizing PVR (MaxP) problem. By exploiting the subproblem structures, a polynomial time approximation algorithm is proposed for MinP, and a polynomial time optimal algorithm is proposed for MaxP. We prove that such a decomposition can provide the 1-alpha approximation ratio, where alpha is the percentage of the police used in MinP. To further improve patrolling efficiency, a grafting mechanism is proposed to integrate the two subproblems' solutions. Finally, we conduct extensive experiments on the real dataset of Foshan, a modern Chinese city. The results demonstrate that compared with benchmarks, our approach scales well to city-scale problem instances with fine-grained periods, hundreds of regions, and hundreds of police officers.

关键词： Patrol planning city-scale decomposition grafting approximation algorithm

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Bicriteria approximation of Chance-Constrained Covering Problems

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OPERATIONS RESEARCH 2020年第2期68卷 516-533页

作者： Xie, Weijun Ahmed, Shabbir Virginia Tech Dept Ind & Syst Engn Blacksburg VA 24061 USA Georgia Inst Technol Sch Ind & Syst Engn Atlanta GA 30332 USA

A chance-constrained optimization problem involves constraints with random data that can be violated with probability bounded from above by a prespecified small risk parameter. Such constraints are used to model reliability requirements in a variety of application areas, such as finance, energy, service, and manufacturing. Except under very special conditions, chance-constrained problems are extremely difficult. There has been a great deal of elegant work on developing tractable approximations of chance constraints. Unfortunately, none of these approaches comes with a constant factor approximation guarantee. We show that such a guarantee is impossible by proving an inapproximability result. By contrast, for a large class of chance-constrained covering problems, we propose a bicriteria approximation scheme. Our scheme finds a solution whose violation probability may be larger than but is within a constant factor of the specified risk parameter and whose objective value is within a constant factor of the true optimal value. Key to our developments is the construction of a tractable convex relaxation of a chance-constrained problem and an appropriate scaling of a solution to this relaxation. We extend our approximation results to the setting in which the underlying distribution of the constraint data is not known. That is, we consider distributionally robust chance-constrained covering problems with convex moment and Wasserstein ambiguity sets and provide bicriteria approximation results.

关键词： chance-constrained problem approximation algorithm distributionally robust optimization convex relaxation

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Approximating a Minimum Dominating Set by Purification

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algorithmS 2024年第6期17卷 258页

作者： Inza, Ernesto Parra Vakhania, Nodari Almira, Jose Maria Sigarreta Hernandez-Aguilar, Jose Alberto Univ Autonoma Estado Morelos Ctr Invest Ciencias Cuernavaca 62209 Morelos Mexico Univ Autonoma Guerrero Fac Matemat Acapulco De Juarez Guerrero Mexico Univ Autonoma Estado Morelos Fac Contaduria Adm & Informat Cuernavaca 62209 Morelos Mexico

A dominating set of a graph is a subset of vertices such that every vertex not in the subset has at least one neighbor within the subset. The corresponding optimization problem is known to be NP-hard. It is proved to be beneficial to separate the solution process in two stages. First, one can apply a fast greedy algorithm to obtain an initial dominating set and then use an iterative procedure to purify (reduce) the size of this dominating set. In this work, we develop the purification stage and propose new purification algorithms. The purification procedures that we present here outperform, in practice, the earlier known purification procedure. We have tested our algorithms for over 1300 benchmark problem instances. Compared to the estimations due to known upper bounds, the obtained solutions are about seven times better. Remarkably, for the 500 benchmark instances for which the optimum is known, the optimal solutions are obtained for 46.33% of the tested instances, whereas the average error for the remaining instances is about 1.01.

关键词： graph theory dominating set approximation algorithm time complexity

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On New Approaches of Maximum Weighted Target Coverage and Sensor Connectivity: Hardness and approximation

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IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING 2020年第3期7卷 1736-1751页

作者： Nguyen, Tu N. Liu, Bing-Hong Wang, Shih-Yuan Purdue Univ Dept Comp Sci Ft Wayne IN 46805 USA Natl Kaohsiung Univ Sci & Technol Dept Elect Engn Kaohsiung 80778 Taiwan

In mobile wireless sensor networks (MWSNs), because the movement of sensors consumes much more power than that in sensing and communication, the problem of scheduling mobile sensors to cover all targets and maintain network connectivity such that the total movement distance of mobile sensors is minimized has received a great deal of attention. However, network design in fact indicates that there are situations (limited budget, sensor failure, or obstacle in a sensing field) in which the number of active mobile sensors is insufficient to cover all targets or form a connected network. Therefore, targets must be weighted by their importance. The more important a target, the higher the weight of the target. A more general problem for target coverage and network connectivity, termed the Maximum Weighted Target Coverage and Sensor Connectivity with Limited Mobile Sensors (TAR-CC) problem, is studied. In this paper, an approximation algorithm, termed the weighted-maximum-coverage-based algorithm (WMCBA), is proposed for the subproblem of the TAR-CC problem. Based on the WMCBA, the Steiner-tree-based algorithm (STBA) is proposed for the TAR-CC problem. Simulation results demonstrate that the STBA provides better performance than the other methods.

关键词： Sensors Wireless sensor networks approximation algorithms Monitoring Schedules Simulation Security Mobile wireless sensor network target coverage network connectivity NP-complete approximation algorithm

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Covering Array on the Cartesian Product of Hypergraphs

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GRAPHS AND COMBINATORICS 2024年第4期40卷 87-87页

作者： Akhtar, Yasmeen Maity, Soumen Birla Inst Technol & Sci Pilani Dept Math K K Birla Goa CampusNH17B Bypass Rd Sancoale 403726 Goa India Indian Inst Sci Educ & Res Dept Math Dr Homi Bhabha Rd Pune 411008 Maharashtra India

Covering array (CA) on a hypergraph H is a combinatorial object used in interaction testing of a complex system modeled as H. Given a t-uniform hypergraph H and positive integer s, it is an array with a column for each vertex having entries from a finite set of cardinality s, such as Z(s), and the property that any set of t columns that correspond to vertices in a hyperedge covers all s(t) ordered t-tuples from Z(s)(t) at least once as a row. Minimizing the number of rows (size) of CA is important in industrial applications. Given a hypergraph H, a CA on H with the minimum size is called optimal. Determining the minimum size of CA on a hypergraph is NP-hard. We focus on constructions that make optimal covering arrays on large hypergraphs from smaller ones and discuss the construction method for optimal CA on the Cartesian product of a Cayley hypergraph with different families of hypergraphs. For a prime power q > 2, we present a polynomial-time approximation algorithm with approximation ratio ([log(q) (vertical bar V vertical bar/3(k-1))])(2) for constructing covering array CA(n, H, q) on 3-uniform hypergraph H = (V, E) with k > 1 prime factors with respect to the Cartesian product.

关键词： Covering array Cartesian product Cayley hypergraph approximation algorithm

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A primal-dual approximation algorithm for the Asymmetric Prize-Collecting TSP

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JOURNAL OF COMBINATORIAL OPTIMIZATION 2013年第2期25卷 265-278页

作者： Viet Hung Nguyen Univ Paris 06 LIP6 Paris France

We present a primal-dual aOElog(n)aOE parts per thousand-approximation algorithm for the version of the asymmetric prize collecting traveling salesman problem, where the objective is to find a directed tour that visits a subset of vertices such that the length of the tour plus the sum of penalties associated with vertices not in the tour is as small as possible. The previous algorithm for the problem (V.H. Nguyen and T.T Nguyen in Int. J. Math. Oper. Res. 4(3):294-301, 2012) which is not combinatorial, is based on the Held-Karp relaxation and heuristic methods such as the Frieze et al.'s heuristic (Frieze et al. in Networks 12:23-39, 1982) or the recent Asadpour et al.'s heuristic for the ATSP (Asadpour et al. in 21st ACM-SIAM symposium on discrete algorithms, 2010). Depending on which of the two heuristics is used, it gives respectively 1+aOElog(n)aOE parts per thousand and as an approximation ratio. Our algorithm achieves an approximation ratio of aOElog(n)aOE parts per thousand which is weaker than but represents the first combinatorial approximation algorithm for the Asymmetric Prize-Collecting TSP.

关键词： Prize collecting Traveling Salesman approximation algorithm Primal-dual algorithm

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algorithms and Complexity for a Class of Combinatorial Optimization Problems with Labelling

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2021年第3期188卷 673-695页

作者： Yang, Zishen Wang, Wei Shi, Majun Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Peoples R China

In this paper, we propose to study a wide class of combinatorial optimization problems called combinatorial optimization problems with labelling. First, we give a combinatorial method to deal with the labelling version of some classical combinatorial optimization problems including minimum vertex cover, maximum independent set, minimum dominating set and minimum set cover, and convert the labelling problems into the original problems by polynomial-time reduction. We show that, although the labelling version of these problem seems more universal than their original counterparts, they are actually equivalent to the corresponding original problem from an algorithmic point of view. Moreover, we generalize the greedy approach for solving submodular cover problem to its labelling version, and as simple applications of our new method, we use it to solve the labelling versions of the minimum weighted spanning tree and connected vertex cover problem in a unified way.

关键词： Combinatorial optimization approximation algorithm Problem labelling Sublobular cover NP-hardness Inapproximation

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A service facility location problem considering customer preference and facility capacity

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COMPUTERS & INDUSTRIAL ENGINEERING 2023年第1期177卷

作者： Kang, Cheng-Nan Kung, Ling-Chieh Chiang, Po-Hsuan Yu, Jiun-Yu Natl Taiwan Univ Master Program Sport Facil Management & Hlth Promo 1 Sect 4 Roosevelt Rd Taipei 10617 Taiwan Natl Taiwan Univ Dept Informat Management 1Sect 4Roosevelt Rd Taipei 10617 Taiwan Natl Taiwan Univ Dept Business Adm 1Sect 4Roosevelt Rd Taipei 10617 Taiwan

Most facility location models do not take customer preferences into account, and are therefore inadequate for application in service facilities. We construct a model to capture customer preferences and maximize the number of customers served. Given a set of open facilities, customers will choose facilities based on their individual preferences. As the problem is NP-hard, we design a heuristic algorithm based on maximum flow. A numerical study demonstrates the algorithm's average performance and general applicability.

关键词： Capacitated facility location Customer preference Maximum flow approximation algorithm

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