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Journal articles on the topic 'Maximum weighted independent set problem'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 February 2022

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1

Wang, Yanfeng, Xuewen Bai, Donghui Wei, and Guangzhao Cui. "DNA Self-Assembly for Maximum Weighted Independent Set Problem." Advanced Science Letters 17, no. 1 (2012): 21–26. http://dx.doi.org/10.1166/asl.2012.3677.

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2

Yu, Chang-Wu, and Gen-Huey Chen. "The weighted maximum independent set problem in permutation graphs." BIT 32, no. 4 (1992): 609–18. http://dx.doi.org/10.1007/bf01994845.

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3

Li, Ruizhi, Yupan Wang, Shuli Hu, Jianhua Jiang, Dantong Ouyang, and Minghao Yin. "Solving the Set Packing Problem via a Maximum Weighted Independent Set Heuristic." Mathematical Problems in Engineering 2020 (December 16, 2020): 1–11. http://dx.doi.org/10.1155/2020/3050714.

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The set packing problem (SPP) is a significant NP-hard combinatorial optimization problem with extensive applications. In this paper, we encode the set packing problem as the maximum weighted independent set (MWIS) problem and solve the encoded problem with an efficient algorithm designed to the MWIS problem. We compare the independent set-based method with the state-of-the-art algorithms for the set packing problem on the 64 standard benchmark instances. The experimental results show that the independent set-based method is superior to the existing algorithms in terms of the quality of the so

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4

Klobučar, Ana, and Robert Manger. "An evolutionary algorithm for the robust maximum weighted independent set problem." Automatika 61, no. 4 (2020): 523–36. http://dx.doi.org/10.1080/00051144.2020.1789364.

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5

Talla Nobibon, Fabrice, and Roel Leus. "Robust maximum weighted independent-set problems on interval graphs." Optimization Letters 8, no. 1 (2012): 227–35. http://dx.doi.org/10.1007/s11590-012-0563-8.

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6

Sakai, Shuichi, Mitsunori Togasaki, and Koichi Yamazaki. "A note on greedy algorithms for the maximum weighted independent set problem." Discrete Applied Mathematics 126, no. 2-3 (2003): 313–22. http://dx.doi.org/10.1016/s0166-218x(02)00205-6.

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7

Klobučar, Ana, and Robert Manger. "Solving Robust Variants of the Maximum Weighted Independent Set Problem on Trees." Mathematics 8, no. 2 (2020): 285. http://dx.doi.org/10.3390/math8020285.

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This paper deals with the maximum weighted independent set (MWIS) problem. We consider several robust variants of the MWIS problem on trees and prove that most of them are NP-hard. We propose a heuristic for solving the considered robust MWIS variants, which is customized for trees. We demonstrate by experiments that our algorithm produces high-quality solutions and runs much faster than a general-purpose optimization software.

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8

LEE, D. T., and MAJID SARRAFZADEH. "MAXIMUM INDEPENDENT SET OF A PERMUTATION GRAPH IN K TRACKS." International Journal of Computational Geometry & Applications 03, no. 03 (1993): 291–304. http://dx.doi.org/10.1142/s021819599300018x.

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A maximum weighted independent set of a permutation graph is a maximum subset of noncrossing chords in a matching diagram (i.e., a set Φ of chords with end-points on two horizontal lines). The problem of finding, among all noncrossing subsets of Φ with density at most k, one with maximum size is considered, where the density of a subset is the maximum number of chords crossing a vertical line and k is a given parameter. A Θ(n log n) time and Θ(n) space algorithm, for solving the problem with n chords, is proposed. As an application, we solve the problem of finding, among all proper subsets wit

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9

Demange, Marc, Bernard Kouakou, and Eric Soutif. "On-line computation and maximum-weighted hereditary subgraph problems." Yugoslav Journal of Operations Research 21, no. 1 (2011): 11–28. http://dx.doi.org/10.2298/yjor1101011d.

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In this paper1 we study the on-line version of maximum-weighted hereditary subgraph problems. In our on-line model, the final instance (a graph with n vertices) is revealed in t clusters, 2 ? t ? n . We first focus on an on-line version of the maximumweighted hereditary subgraph problem. Then, we deal with the particular case of the independent set problem. We are interested in two types of results: the competitive ratio guaranteed by the on-line algorithm and hardness results that account for the difficulty of the problems and for the quality of algorithms developed to solve them.

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10

Haunert, Jan-Henrik, and Alexander Wolff. "BEYOND MAXIMUM INDEPENDENT SET: AN EXTENDED MODEL FOR POINT-FEATURE LABEL PLACEMENT." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLI-B2 (June 7, 2016): 109–14. http://dx.doi.org/10.5194/isprsarchives-xli-b2-109-2016.

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Map labeling is a classical problem of cartography that has frequently been approached by combinatorial optimization. Given a set of features in the map and for each feature a set of label candidates, a common problem is to select an independent set of labels (that is, a labeling without label–label overlaps) that contains as many labels as possible and at most one label for each feature. To obtain solutions of high cartographic quality, the labels can be weighted and one can maximize the total weight (rather than the number) of the selected labels. We argue, however, that when maximizing the

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11

Haunert, Jan-Henrik, and Alexander Wolff. "BEYOND MAXIMUM INDEPENDENT SET: AN EXTENDED MODEL FOR POINT-FEATURE LABEL PLACEMENT." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLI-B2 (June 7, 2016): 109–14. http://dx.doi.org/10.5194/isprs-archives-xli-b2-109-2016.

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Map labeling is a classical problem of cartography that has frequently been approached by combinatorial optimization. Given a set of features in the map and for each feature a set of label candidates, a common problem is to select an independent set of labels (that is, a labeling without label–label overlaps) that contains as many labels as possible and at most one label for each feature. To obtain solutions of high cartographic quality, the labels can be weighted and one can maximize the total weight (rather than the number) of the selected labels. We argue, however, that when maximizing the

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12

Afif, Mohamed, Aristidis Likas, and Vangelis Th Paschos. "A natural model and a parallel algorithm for approximately solving the maximum weighted independent set problem." Chaos, Solitons & Fractals 5, no. 5 (1995): 739–46. http://dx.doi.org/10.1016/0960-0779(94)00175-p.

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13

Lu, Ling-Xia, and Bei Zhang. "Graphs and Matroids Weighted in a Bounded Incline Algebra." Scientific World Journal 2014 (2014): 1–4. http://dx.doi.org/10.1155/2014/912715.

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Firstly, for a graph weighted in a bounded incline algebra (or called a dioid), a longest path problem (LPP, for short) is presented, which can be considered the uniform approach to the famous shortest path problem, the widest path problem, and the most reliable path problem. The solutions for LPP and related algorithms are given. Secondly, for a matroid weighted in a linear matroid, the maximum independent set problem is studied.

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14

Koh, Zhuan Khye, and Laura Sanità. "Stabilizing Weighted Graphs." Mathematics of Operations Research 45, no. 4 (2020): 1318–41. http://dx.doi.org/10.1287/moor.2019.1034.

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An edge-weighted graph [Formula: see text] is called stable if the value of a maximum-weight matching equals the value of a maximum-weight fractional matching. Stable graphs play an important role in network bargaining games and cooperative matching games, because they characterize instances that admit stable outcomes. We give the first polynomial-time algorithm to find a minimum cardinality subset of vertices whose removal from G yields a stable graph, for any weighted graph G. The algorithm is combinatorial and exploits new structural properties of basic fractional matchings, which are of in

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15

Kahribt, Tahani Jabbar, and Mohammed Kadhim Al- Zuwaini. "Branch and Bound Method to Solve Multi Objectives Function." JOURNAL OF ADVANCES IN MATHEMATICS 12, no. 3 (2016): 5964–74. http://dx.doi.org/10.24297/jam.v12i3.494.

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This paper presents a branch and bound algorithm for sequencing a set of n independent jobs on a single machine to minimize sum of the discounted total weighted completion time and maximum lateness, this problems is NP-hard. Two lower bounds were proposed and heuristic method to get an upper bound. Some special cases were proved and some dominance rules were suggested and proved, the problem solved with up to 50 jobs.

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16

Hifi, M. "A Genetic Algorithm-Based Heuristic for Solving the Weighted Maximum Independent Set and Some Equivalent Problems." Journal of the Operational Research Society 48, no. 6 (1997): 612. http://dx.doi.org/10.2307/3010225.

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17

Hifi, M. "A genetic algorithm-based heuristic for solving the weighted maximum independent set and some equivalent problems." Journal of the Operational Research Society 48, no. 6 (1997): 612–22. http://dx.doi.org/10.1038/sj.jors.2600405.

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18

Hifi, M. "A genetic algorithm-based heuristic for solving the weighted maximum independent set and some equivalent problems." Journal of the Operational Research Society 48, no. 6 (1997): 612–22. http://dx.doi.org/10.1057/palgrave.jors.2600405.

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19

SARRAFZADEH, MAJID, and D. T. LEE. "RESTRICTED TRACK ASSIGNMENT WITH APPLICATIONS." International Journal of Computational Geometry & Applications 04, no. 01 (1994): 53–68. http://dx.doi.org/10.1142/s0218195994000057.

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Consider a set of intervals S = {I1, I2, …, In}, where Ii = (li, ri), li, and ri are real numbers, and li < ri. We study a restricted track assignment problem (RTAP): if an interval Ia contains another interval Ib, then Ia must be assigned to a higher track than Ib, and the goal is to minimize the number of tracks used. The problem RTAP is shown to be NP-hard. An approximation algorithm that produces a solution within twice of the optimal is also presented and the bound is shown to be tight. The algorithm runs in O(n log n) time and requires linear space. The proposed approximation algorith

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20

Li, Shi-Sheng, De-Liang Qian, and Ren-Xia Chen. "Proportionate Flow Shop Scheduling with Rejection." Asia-Pacific Journal of Operational Research 34, no. 04 (2017): 1750015. http://dx.doi.org/10.1142/s0217595917500154.

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We consider the problem of scheduling [Formula: see text] jobs with rejection on a set of [Formula: see text] machines in a proportionate flow shop system where the job processing times are machine-independent. The goal is to find a schedule to minimize the scheduling cost of all accepted jobs plus the total penalty of all rejected jobs. Two variations of the scheduling cost are considered. The first is the maximum tardiness and the second is the total weighted completion time. For the first problem, we first show that it is [Formula: see text]-hard, then we construct a pseudo-polynomial time

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21

Zhao, Zeyu, and John P. Dickerson. "Clearing Kidney Exchanges via Graph Neural Network Guided Tree Search (Student Abstract)." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 10 (2020): 13989–90. http://dx.doi.org/10.1609/aaai.v34i10.7267.

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Kidney exchange is an organized barter market that allows patients with end-stage renal disease to trade willing donors—and thus kidneys—with other patient-donor pairs. The central clearing problem is to find an arrangement of swaps that maximizes the number of transplants. It is known to be NP-hard in almost all cases. Most existing approaches have modeled this problem as a mixed integer program (MIP), using classical branch-and-price-based tree search techniques to optimize. In this paper, we frame the clearing problem as a Maximum Weighted Independent Set (MWIS) problem, and use a Graph Neu

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22

Fomin, Fedor V., and Petr A. Golovach. "Subexponential Parameterized Algorithms and Kernelization on Almost Chordal Graphs." Algorithmica 83, no. 7 (2021): 2170–214. http://dx.doi.org/10.1007/s00453-021-00822-x.

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AbstractWe study algorithmic properties of the graph class $${\textsc {Chordal}}{-ke}$$ C H O R D A L - k e , that is, graphs that can be turned into a chordal graph by adding at most k edges or, equivalently, the class of graphs of fill-in at most k. It appears that a number of fundamental intractable optimization problems being parameterized by k admit subexponential algorithms on graphs from $${\textsc {Chordal}}{-ke}$$ C H O R D A L - k e . More precisely, we identify a large class of optimization problems on $${\textsc {Chordal}}{-ke}$$ C H O R D A L - k e solvable in time $$2^{{\mathcal{

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23

Zhang, Chu, Chaoshun Li, Tian Peng, et al. "Modeling and Synchronous Optimization of Pump Turbine Governing System Using Sparse Robust Least Squares Support Vector Machine and Hybrid Backtracking Search Algorithm." Energies 11, no. 11 (2018): 3108. http://dx.doi.org/10.3390/en11113108.

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In view of the complex and changeable operating environment of pumped storage power stations and the noise and outliers in the modeling data, this study proposes a sparse robust least squares support vector machine (LSSVM) model based on the hybrid backtracking search algorithm for the model identification of a pumped turbine governing system. By introducing the maximum linearly independent set, the sparsity of the support vectors of the LSSVM model are realized, and the complexity is reduced. The robustness of the identification model to noise and outliers is enhanced using the weighted funct

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24

Luo, Dong Ling, Chen Yin Wang, Yang Yi, Dong Ling Zhang, and Xiao Cong Zhou. "Fuzzy Maximum Independent Set Problem." Applied Mechanics and Materials 687-691 (November 2014): 1161–65. http://dx.doi.org/10.4028/www.scientific.net/amm.687-691.1161.

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Edge covering problem, dominating set problem, and independent set problem are classic problems in graph theory except for vertex covering problem. In this paper, we study the maximum independent set problem under fuzzy uncertainty environments, which aims to search for the independent set with maximum value in a graph. First, credibility theory is introduced to describe the fuzzy variable. Three decision models are performed based on the credibility theory. A hybrid intelligence algorithm which integrates genetic algorithm and fuzzy simulation is proposed due to the unavailability of traditio

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25

Luo, Dong Ling, Chen Yin Wang, Yang Yi, Dong Ling Zhang, and Xiao Cong Zhou. "Fuzzy Maximum Independent Set Problem of Graphic." Applied Mechanics and Materials 687-691 (November 2014): 1657–61. http://dx.doi.org/10.4028/www.scientific.net/amm.687-691.1657.

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Edge covering problem, dominating set problem, and independent set problem are classic problems in graph theory except for vertex covering problem. In this paper, we study the maximum independent set problem under fuzzy uncertainty environments, which aims to search for the independent set with maximum value in a graph. First, credibility theory is introduced to describe the fuzzy variable. Three decision models are performed based on the credibility theory. A hybrid intelligence algorithm which integrates genetic algorithm and fuzzy simulation is proposed due to the unavailability of traditio

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26

Lee, Chuan-Min. "Weighted Maximum-Clique Transversal Sets of Graphs." ISRN Discrete Mathematics 2011 (January 26, 2011): 1–20. http://dx.doi.org/10.5402/2011/540834.

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A maximum-clique transversal set of a graph G is a subset of vertices intersecting all maximum cliques of G. The maximum-clique transversal set problem is to find a maximum-clique transversal set of G of minimum cardinality. Motivated by the placement of transmitters for cellular telephones, Chang, Kloks, and Lee introduced the concept of maximum-clique transversal sets on graphs in 2001. In this paper, we study the weighted version of the maximum-clique transversal set problem for split graphs, balanced graphs, strongly chordal graph, Helly circular-arc graphs, comparability graphs, distance-

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27

FAN, Yue-Ke, Xiao-Li Qiang, and Jin XU. "Sticker Model for Maximum Clique Problem and Maximum Independent Set." Chinese Journal of Computers 33, no. 2 (2010): 305–10. http://dx.doi.org/10.3724/sp.j.1016.2010.00305.

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28

Saha, Anita, and Madhumangal Pal. "Maximum weightk-independent set problem on permutation graphs." International Journal of Computer Mathematics 80, no. 12 (2003): 1477–87. http://dx.doi.org/10.1080/00207160310001614972.

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29

Yang, Yan, and Zhi Xiang Yin. "Surface- Based Computing Model of Maximum Independent Set Problem." Advanced Materials Research 328-330 (September 2011): 1729–33. http://dx.doi.org/10.4028/www.scientific.net/amr.328-330.1729.

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About thirty years ago, the concept of the complexity of the problem was proposed. The most important complex class is P and NP class. Fruitful results of this concept are the existence of the so-called complex class complete problem. If the other issues of this class once solved in polynomial time, then the problem must exist polynomial time algorithms. Therefore, the complete problem is most difficult to solve, but because of their presence, we can choose any of them improved algorithm for a problem, so this kind of problem to get a good solution. DNA computing is a novel method that solving

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30

Andrade, Diogo V., Mauricio G. C. Resende, and Renato F. Werneck. "Fast local search for the maximum independent set problem." Journal of Heuristics 18, no. 4 (2012): 525–47. http://dx.doi.org/10.1007/s10732-012-9196-4.

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31

Burns, James E. "The maximum independent set problem for cubic planar graphs." Networks 19, no. 3 (1989): 373–78. http://dx.doi.org/10.1002/net.3230190307.

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32

Kako, Akihisa, Takao Ono, Tomio Hirata, and Magnús M. Halldórsson. "Approximation algorithms for the weighted independent set problem in sparse graphs." Discrete Applied Mathematics 157, no. 4 (2009): 617–26. http://dx.doi.org/10.1016/j.dam.2008.08.027.

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33

Goldengorin, B. I., D. S. Malyshev, P. M. Pardalos, and V. A. Zamaraev. "A tolerance-based heuristic approach for the weighted independent set problem." Journal of Combinatorial Optimization 29, no. 2 (2013): 433–50. http://dx.doi.org/10.1007/s10878-013-9606-z.

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34

Lê, Ngoc C., and Trung Tran. "On the Maximum Independent Set Problem in Graphs of Bounded Maximum Degree." Acta Mathematica Vietnamica 45, no. 2 (2020): 463–75. http://dx.doi.org/10.1007/s40306-020-00368-0.

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35

Brause, Christoph, Ngoc C. Le, and Ingo Schiermeyer. "On sequential heurestic methods for the maximum independent set problem." Discussiones Mathematicae Graph Theory 37, no. 2 (2017): 415. http://dx.doi.org/10.7151/dmgt.1965.

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36

Murat, Cécile, and Vangelis Th Paschos. "A priori optimization for the probabilistic maximum independent set problem." Theoretical Computer Science 270, no. 1-2 (2002): 561–90. http://dx.doi.org/10.1016/s0304-3975(01)00005-6.

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37

Butenko, Sergiy, and Svyatoslav Trukhanov. "Using critical sets to solve the maximum independent set problem." Operations Research Letters 35, no. 4 (2007): 519–24. http://dx.doi.org/10.1016/j.orl.2006.07.004.

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38

Tang Jian. "An O(20.304n) Algorithm for Solving Maximum Independent Set Problem." IEEE Transactions on Computers C-35, no. 9 (1986): 847–51. http://dx.doi.org/10.1109/tc.1986.1676847.

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39

Shiraishi, Naoto, and Jun Takahashi. "Constructing concrete hard instances of the maximum independent set problem." Journal of Statistical Mechanics: Theory and Experiment 2019, no. 11 (2019): 113401. http://dx.doi.org/10.1088/1742-5468/ab409d.

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40

Paschos, V. Th. "A ( °/2) -approximation algorithm for the maximum independent set problem." Information Processing Letters 44, no. 1 (1992): 11–13. http://dx.doi.org/10.1016/0020-0190(92)90248-t.

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41

Brause, Christoph, Ngoc Chi Lê, and Ingo Schiermeyer. "The Maximum Independent Set Problem in Subclasses of Subcubic Graphs." Discrete Mathematics 338, no. 10 (2015): 1766–78. http://dx.doi.org/10.1016/j.disc.2015.01.041.

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42

Barbosa, Valmir C., and Luciana C. D. Campos. "A Novel Evolutionary Formulation of the Maximum Independent Set Problem." Journal of Combinatorial Optimization 8, no. 4 (2004): 419–37. http://dx.doi.org/10.1007/s10878-004-4835-9.

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43

Chieu, H. L., and W. S. Lee. "Relaxed Survey Propagation for The Weighted Maximum Satisfiability Problem." Journal of Artificial Intelligence Research 36 (October 30, 2009): 229–66. http://dx.doi.org/10.1613/jair.2808.

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The survey propagation (SP) algorithm has been shown to work well on large instances of the random 3-SAT problem near its phase transition. It was shown that SP estimates marginals over covers that represent clusters of solutions. The SP-y algorithm generalizes SP to work on the maximum satisfiability (Max-SAT) problem, but the cover interpretation of SP does not generalize to SP-y. In this paper, we formulate the relaxed survey propagation (RSP) algorithm, which extends the SP algorithm to apply to the weighted Max-SAT problem. We show that RSP has an interpretation of estimating marginals ov

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44

Milanič, Martin, and Jérôme Monnot. "The Exact Weighted Independent Set Problem in Perfect Graphs and Related Classes." Electronic Notes in Discrete Mathematics 35 (December 2009): 317–22. http://dx.doi.org/10.1016/j.endm.2009.11.052.

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45

Gol’dengorin, B. I., D. S. Malyshev, and P. M. Pardalos. "Efficient computation of tolerances in the weighted independent set problem for trees." Doklady Mathematics 87, no. 3 (2013): 368–71. http://dx.doi.org/10.1134/s1064562413030186.

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46

Pardalos, Panos M., and Nisha Desai. "An algorithm for finding a maximum weighted independent set in an arbitrary graph." International Journal of Computer Mathematics 38, no. 3-4 (1991): 163–75. http://dx.doi.org/10.1080/00207169108803967.

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47

Joo, Changhee, Xiaojun Lin, Jiho Ryu, and Ness B. Shroff. "Distributed Greedy Approximation to Maximum Weighted Independent Set for Scheduling With Fading Channels." IEEE/ACM Transactions on Networking 24, no. 3 (2016): 1476–88. http://dx.doi.org/10.1109/tnet.2015.2417861.

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48

Avenali, Alessandro. "Resolution Branch and Bound and an Application: The Maximum Weighted Stable Set Problem." Operations Research 55, no. 5 (2007): 932–48. http://dx.doi.org/10.1287/opre.1070.0397.

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49

Ugurlu, Onur. "A New Heuristic Algorithm to Solve the Maximum Independent Set Problem." Mathematical and Computational Applications 18, no. 3 (2013): 495–501. http://dx.doi.org/10.3390/mca18030495.

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50

Douiri, Sidi Mohamed, and Souad Elbernoussi. "An unconstrained binary quadratic programming for the maximum independent set problem." Nonlinear Analysis: Modelling and Control 17, no. 4 (2012): 410–17. http://dx.doi.org/10.15388/na.17.4.14047.

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For a given graph G = (V, E) the maximum independent set problem is to find the largest subset of pairwise nonadjacent vertices. We propose a new model which is a reformulation of the maximum independent set problem as an unconstrained quadratic binary programming, and we resolve it afterward by means of a genetic algorithm. The efficiency of the approach is confirmed by results of numerical experiments on DIMACS benchmarks.

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