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Journal articles on the topic 'Set covering'

Author: Grafiati

Published: 4 June 2021

Last updated: 22 February 2023

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1

Jones, Lenny, and Daniel White. "On primitive covering numbers." International Journal of Number Theory 13, no. 01 (November 16, 2016): 27–37. http://dx.doi.org/10.1142/s1793042117500038.

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In 2007, Zhi-Wei Sun defined a covering number to be a positive integer [Formula: see text] such that there exists a covering system of the integers where the moduli are distinct divisors of [Formula: see text] greater than 1. A covering number [Formula: see text] is called primitive if no proper divisor of [Formula: see text] is a covering number. Sun constructed an infinite set [Formula: see text] of primitive covering numbers, and he conjectured that every primitive covering number must satisfy a certain condition. In this paper, for a given [Formula: see text], we derive a formula that gives the exact number of coverings that have [Formula: see text] as the least common multiple of the set [Formula: see text] of moduli, under certain restrictions on [Formula: see text]. Additionally, we disprove Sun’s conjecture by constructing an infinite set of primitive covering numbers that do not satisfy his primitive covering number condition.

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2

Lombardi, Michele. "Minimal covering set solutions." Social Choice and Welfare 32, no. 4 (December 20, 2008): 687–95. http://dx.doi.org/10.1007/s00355-008-0361-5.

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3

Lefkovitch, L. P. "Entropy and set covering." Information Sciences 36, no. 3 (September 1985): 283–94. http://dx.doi.org/10.1016/0020-0255(85)90058-1.

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4

ZIMMERMANN, KAREL. "FUZZY SET COVERING PROBLEM." International Journal of General Systems 20, no. 1 (December 1991): 127–31. http://dx.doi.org/10.1080/03081079108945020.

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5

Havrda, Jan. "Projection and covering in a set with orthogonality." Časopis pro pěstování matematiky 112, no. 3 (1987): 245–48. http://dx.doi.org/10.21136/cpm.1987.118319.

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6

Ma, Zhengyu, Kedong Yan, Kwangsoo Kim, and Hong Seo Ryoo. "Set Covering-based Feature Selection of Large-scale Omics Data." Journal of the Korean Operations Research and Management Science Society 39, no. 4 (November 30, 2014): 75–84. http://dx.doi.org/10.7737/jkorms.2014.39.4.075.

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7

Chang, H. C., and N. Prabhu. "Set covering number for a finite set." Bulletin of the Australian Mathematical Society 53, no. 2 (April 1996): 267–69. http://dx.doi.org/10.1017/s0004972700016981.

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Given a finite set S of cardinality N, the minimum number of j-subsets of S needed to cover all the r-subsets of S is called the covering number C(N, j, r). While Erdös and Hanani's conjecture that was proved by Rödl, no nontrivial upper bound for C(N, j, r) was known for finite N. In this note we obtain a nontrivial upper bound by showing that for finite N,

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8

Beraldi, Patrizia, and Andrzej Ruszczyński. "The Probabilistic Set-Covering Problem." Operations Research 50, no. 6 (December 2002): 956–67. http://dx.doi.org/10.1287/opre.50.6.956.345.

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9

Ahmed, Shabbir, and Dimitri J. Papageorgiou. "Probabilistic Set Covering with Correlations." Operations Research 61, no. 2 (April 2013): 438–52. http://dx.doi.org/10.1287/opre.1120.1135.

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10

Brandt, Felix, and Felix Fischer. "Computing the minimal covering set." Mathematical Social Sciences 56, no. 2 (September 2008): 254–68. http://dx.doi.org/10.1016/j.mathsocsci.2008.04.001.

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11

Clarke, R. J. "Covering a set by subsets." Discrete Mathematics 81, no. 2 (April 1990): 147–52. http://dx.doi.org/10.1016/0012-365x(90)90146-9.

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12

Mannino, Carlo, and Antonio Sassano. "Solving hard set covering problems." Operations Research Letters 18, no. 1 (August 1995): 1–5. http://dx.doi.org/10.1016/0167-6377(95)00034-h.

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13

Yao, Yiyu, and Bingxue Yao. "Covering based rough set approximations." Information Sciences 200 (October 2012): 91–107. http://dx.doi.org/10.1016/j.ins.2012.02.065.

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14

Kwatera, Renata Krystyna, and Bruno Simeone. "Clustering heuristics for set covering." Annals of Operations Research 43, no. 5 (May 1993): 295–308. http://dx.doi.org/10.1007/bf02025300.

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15

Sherali, Hanif D., Seong-In Kim, and Edna L. Parrish. "Probabilistic partial set covering problems." Naval Research Logistics 38, no. 1 (February 1991): 41–51. http://dx.doi.org/10.1002/1520-6750(199102)38:1<41::aid-nav3220380106>3.0.co;2-l.

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16

Mikhailyuk, V. A. "Reoptimization of set covering problems." Cybernetics and Systems Analysis 46, no. 6 (November 2010): 879–83. http://dx.doi.org/10.1007/s10559-010-9269-z.

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17

Kampel, Ludwig, Bernhard Garn, and Dimitris E. Simos. "Covering Arrays via Set Covers." Electronic Notes in Discrete Mathematics 65 (March 2018): 11–16. http://dx.doi.org/10.1016/j.endm.2018.02.014.

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18

Ekim*, Tinaz, and Vangelis Th Paschos. "Approximation preserving reductions for set covering, vertex covering and independent set hierarchies under differential approximationa." International Journal of Computer Mathematics 81, no. 5 (May 2004): 569–82. http://dx.doi.org/10.1080/00207160410001688592.

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19

You, Xiaoying, Jinjin Li, and Hongkun Wang. "Relative Reduction of Neighborhood-Covering Pessimistic Multigranulation Rough Set Based on Evidence Theory." Information 10, no. 11 (October 29, 2019): 334. http://dx.doi.org/10.3390/info10110334.

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Relative reduction of multiple neighborhood-covering with multigranulation rough set has been one of the hot research topics in knowledge reduction theory. In this paper, we explore the relative reduction of covering information system by combining the neighborhood-covering pessimistic multigranulation rough set with evidence theory. First, the lower and upper approximations of multigranulation rough set in neighborhood-covering information systems are introduced based on the concept of neighborhood of objects. Second, the belief and plausibility functions from evidence theory are employed to characterize the approximations of neighborhood-covering multigranulation rough set. Then the relative reduction of neighborhood-covering information system is investigated by using the belief and plausibility functions. Finally, an algorithm for computing a relative reduction of neighborhood-covering pessimistic multigranulation rough set is proposed according to the significance of coverings defined by the belief function, and its validity is examined by a practical example.

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20

Vasanthi, R., and K. Subramanian. "On the minimum vertex covering transversal dominating sets in graphs and their classification." Discrete Mathematics, Algorithms and Applications 09, no. 05 (October 2017): 1750069. http://dx.doi.org/10.1142/s1793830917500690.

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Let [Formula: see text] be a simple and connected graph. A dominating set [Formula: see text] is said to be a vertex covering transversal dominating set if it intersects every minimum vertex covering set of [Formula: see text]. The vertex covering transversal domination number [Formula: see text] is the minimum cardinality among all vertex covering transversal dominating sets of [Formula: see text]. A vertex covering transversal dominating set of minimum cardinality [Formula: see text] is called a minimum vertex covering transversal dominating set or simply a [Formula: see text]-set. In this paper, we prove some general theorems on the vertex covering transversal domination number of a simple connected graph. We also provide some results about [Formula: see text]-sets and try to classify those sets based on their intersection with the minimum vertex covering sets.

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21

Amaldi, Edoardo, Sandro Bosio, and Federico Malucelli. "Hyperbolic set covering problems with competing ground-set elements." Mathematical Programming 134, no. 2 (January 30, 2011): 323–48. http://dx.doi.org/10.1007/s10107-010-0431-1.

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22

Saffari, Saeed, and Yahya Fathi. "Set covering problem with conflict constraints." Computers & Operations Research 143 (July 2022): 105763. http://dx.doi.org/10.1016/j.cor.2022.105763.

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23

Parida, Kedar Chandra, Debadutta Mohanty, and Nilaratna Kalia. "Soft Rough Set With Covering Based." Global Journal of Pure and Applied Mathematics 16, no. 6 (December 30, 2020): 939. http://dx.doi.org/10.37622/gjpam/16.6.2020.939-946.

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24

Volna, Eva, and Martin Kotyrba. "Evolutionary Optimization of Set-Covering Problem." Applied Mathematics & Information Sciences 10, no. 4 (July 1, 2016): 1293–301. http://dx.doi.org/10.18576/amis/100408.

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25

Grandoni, Fabrizio, Anupam Gupta, Stefano Leonardi, Pauli Miettinen, Piotr Sankowski, and Mohit Singh. "Set Covering with Our Eyes Closed." SIAM Journal on Computing 42, no. 3 (January 2013): 808–30. http://dx.doi.org/10.1137/100802888.

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26

Hwang, M. J., C. I. Chiang, and Y. H. Liu. "Solving a fuzzy set-covering problem." Mathematical and Computer Modelling 40, no. 7-8 (October 2004): 861–65. http://dx.doi.org/10.1016/j.mcm.2004.10.015.

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27

Bergantiños, Gustavo, María Gómez-Rúa, Natividad Llorca, Manuel Pulido, and Joaquín Sánchez-Soriano. "Allocating costs in set covering problems." European Journal of Operational Research 284, no. 3 (August 2020): 1074–87. http://dx.doi.org/10.1016/j.ejor.2020.01.031.

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28

Monfroglio, Angelo. "Hybrid heuristic algorithms for Set Covering." Computers & Operations Research 25, no. 6 (June 1998): 441–55. http://dx.doi.org/10.1016/s0305-0548(97)00084-1.

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29

Hua, Qiang-Sheng, Yuexuan Wang, Dongxiao Yu, and Francis C. M. Lau. "Set multi-covering via inclusion–exclusion." Theoretical Computer Science 410, no. 38-40 (September 2009): 3882–92. http://dx.doi.org/10.1016/j.tcs.2009.05.020.

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30

Panteli, Antiopi, Basilis Boutsinas, and Ioannis Giannikos. "On Set Covering Based on Biclustering." International Journal of Information Technology & Decision Making 13, no. 05 (September 2014): 1029–49. http://dx.doi.org/10.1142/s0219622014500692.

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In this paper, we present a clustering heuristic for solving demand covering models where the objective is to determine locations for servers that optimally cover a given set of demand points. This heuristic is based on the concept of biclusters and processes the set of demand points as well as the set of potential servers and determines biclusters that result in smaller problems. Given a coverage matrix, a bicluster is defined as a sub-matrix spanned by both a subset of rows and a subset of columns, such that rows are the most similar to each other when compared over columns. The algorithm starts by using any biclustering algorithm in order to identify appropriate biclusters of the coverage matrix and then combines selected biclusters to define an aggregate solution to the original problem. The algorithm can be easily adapted to address a whole family of covering problems including set covering, maximal covering and backup covering problems. The proposed algorithm is tested in a series of widely known test datasets for various such problems. The main objective of this paper is to introduce the concept of biclustering as an efficient and effective approach to tackle covering problems and to stimulate further research in this area.

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31

Zhou, Kang, and Jin Chen. "Simulation DNA Algorithm of Set Covering." Applied Mathematics & Information Sciences 8, no. 1 (January 1, 2014): 139–44. http://dx.doi.org/10.12785/amis/080117.

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32

Krivelevich, Michael. "Approximate Set Covering in Uniform Hypergraphs." Journal of Algorithms 25, no. 1 (October 1997): 118–43. http://dx.doi.org/10.1006/jagm.1997.0872.

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33

Senthil Kumar, S., H. Hannah Inbarani, Ahmad Taher Azar, and Kemal Polat. "Covering-based rough set classification system." Neural Computing and Applications 28, no. 10 (June 14, 2016): 2879–88. http://dx.doi.org/10.1007/s00521-016-2412-7.

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34

Haddadi, S. "Benders decomposition for set covering problems." Journal of Combinatorial Optimization 33, no. 1 (July 22, 2015): 60–80. http://dx.doi.org/10.1007/s10878-015-9935-1.

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35

Beasley, J. E. "An algorithm for set covering problem." European Journal of Operational Research 31, no. 1 (July 1987): 85–93. http://dx.doi.org/10.1016/0377-2217(87)90141-x.

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36

Kočinac, Ljubiša D. R., Şukran Konca, and Sumit Singh. "Set Star-Menger and Set Strongly Star-Menger Spaces." Mathematica Slovaca 72, no. 1 (February 1, 2022): 185–96. http://dx.doi.org/10.1515/ms-2022-0013.

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Abstract Motivated by the Arhangel’skii “s-Lindelöf cardinal function” definition, Kočinac and Konca defined and studied set covering properties and set star covering properties. In this paper, we present results on the star covering properties called set star-Menger and set strongly star-Menger. We investigate the relationship among set star-Menger, set strongly star-Menger and other related properties and study the topological properties of set star-Menger and set strongly star-Menger properties.

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37

Han, Sang-Eon. "Covering rough set structures for a locally finite covering approximation space." Information Sciences 480 (April 2019): 420–37. http://dx.doi.org/10.1016/j.ins.2018.12.049.

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38

Dai, Jianhua, Debiao Huang, Huashi Su, Haowei Tian, and Tian Yang. "Uncertainty Measurement for Covering Rough Sets." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 22, no. 02 (April 2014): 217–33. http://dx.doi.org/10.1142/s021848851450010x.

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Covering rough set theory is an important generalization of traditional rough set theory. So far, the studies on covering generalized rough sets mainly focus on constructing different types of approximation operations. However, little attention has been paid to uncertainty measurement in covering cases. In this paper, a new kind of partial order is proposed for coverings which is used to evaluate the uncertainty measures. Consequently, we study uncertain measures like roughness measure, accuracy measure, entropy and granularity for covering rough set models which are defined by neighborhoods and friends. Some theoretical results are obtained and investigated.

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39

Liu, Guilong, and William Zhu. "Approximations in Rough Sets vs Granular Computing for Coverings." International Journal of Cognitive Informatics and Natural Intelligence 4, no. 2 (April 2010): 63–76. http://dx.doi.org/10.4018/jcini.2010040105.

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Rough set theory is an important technique in knowledge discovery in databases. Classical rough set theory proposed by Pawlak is based on equivalence relations, but many interesting and meaningful extensions have been made based on binary relations and coverings, respectively. This paper makes a comparison between covering rough sets and rough sets based on binary relations. This paper also focuses on the authors’ study of the condition under which the covering rough set can be generated by a binary relation and the binary relation based rough set can be generated by a covering.

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40

Paschos, V. Th. "A relation between the approximated versions of minimum set covering, minimum vertex covering and maximum independent set." RAIRO - Operations Research 28, no. 4 (1994): 413–33. http://dx.doi.org/10.1051/ro/1994280404131.

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41

Zhu, Yanqing, and William Zhu. "A Variable Precision Covering-Based Rough Set Model Based on Functions." Scientific World Journal 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/210129.

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Classical rough set theory is a technique of granular computing for handling the uncertainty, vagueness, and granularity in information systems. Covering-based rough sets are proposed to generalize this theory for dealing with covering data. By introducing a concept of misclassification rate functions, an extended variable precision covering-based rough set model is proposed in this paper. In addition, we define thef-lower andf-upper approximations in terms of neighborhoods in the extended model and study their properties. Particularly, two coverings with the same reductions are proved to generate the samef-lower andf-upper approximations. Finally, we discuss the relationships between the new model and some other variable precision rough set models.

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42

Xu, Qingyuan, Anhui Tan, and Yaojin Lin. "A rough set method for the unicost set covering problem." International Journal of Machine Learning and Cybernetics 8, no. 3 (May 3, 2015): 781–92. http://dx.doi.org/10.1007/s13042-015-0365-2.

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43

El-Darzi, E., and G. Mitra. "Set covering and set partitioning: A collection of test problems." Omega 18, no. 2 (January 1990): 195–201. http://dx.doi.org/10.1016/0305-0483(90)90066-i.

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44

El-Darzi, Elia, and Gautam Mitra. "Graph theoretic relaxations of set covering and set partitioning problems." European Journal of Operational Research 87, no. 1 (November 1995): 109–21. http://dx.doi.org/10.1016/0377-2217(94)00115-s.

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45

Zhang, Yan-Lan, and Chang-Qing Li. "Numerical Characterizations of Topological Reductions of Covering Information Systems in Evidence Theory." Mathematical Problems in Engineering 2021 (March 31, 2021): 1–9. http://dx.doi.org/10.1155/2021/6648108.

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The reductions of covering information systems in terms of covering approximation operators are one of the most important applications of covering rough set theory. Based on the connections between the theory of topology and the covering rough set theory, two kinds of topological reductions of covering information systems are discussed in this paper, which are characterized by the belief and plausibility functions from the evidence theory. The topological spaces by two pairs of covering approximation operators in covering information systems are pseudo-discrete, which deduce partitions. Then, using plausibility function values of the sets in the partitions, the definitions of significance and relative significance of coverings are presented. Hence, topological reduction algorithms based on the evidence theory are proposed in covering information systems, and an example is adopted to illustrate the validity of the algorithms.

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46

Wang, Zhaohao. "Comparative Studies of Covering Rough Set Models." Mathematical Problems in Engineering 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/502724.

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Many different proposals exist for the definition of lower and upper approximation operators in covering-based rough sets and so many different covering rough set models are built correspondingly. It is meaningful to explore the connection of these covering rough set models for their applications in practice. In this paper, we establish relationships between the most commonly used operators in covering rough set models. We investigate the conditions under which two types of upper approximation operations are identical.

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47

HU, Jun, Guo-Yin WANG, and Qing-Hua ZHANG. "Covering Based Generalized Rough Fuzzy Set Model." Journal of Software 21, no. 5 (May 14, 2010): 968–77. http://dx.doi.org/10.3724/sp.j.1001.2010.2010.03624.

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48

Guo, Liucheng, David B. Thomas, and Wayne Luk. "Customisable architectures for the set covering problem." ACM SIGARCH Computer Architecture News 41, no. 5 (December 18, 2013): 101–6. http://dx.doi.org/10.1145/2641361.2641378.

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49

Kruger, A. Ya. "A covering theorem for set-valued mappings." Optimization 19, no. 6 (January 1988): 763–80. http://dx.doi.org/10.1080/02331938808843391.

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50

Wang, Longwu, and Zengtai Gong. "Covering-Based Grade Rough Fuzzy Set Models." Journal of Mathematics and Informatics 16 (March 31, 2019): 1–11. http://dx.doi.org/10.22457/jmi.134av16a1.

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