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Coloring and Maximum Independent Set of Rectangles
2011In this paper, we consider two geometric optimization problems: Rectangle Coloring problem (RCOL) and Maximum Independent Set of Rectangles (MISR). In RCOL, we are given a collection of n rectangles in the plane where overlapping rectangles need to be colored differently, and the goal is to find a coloring using minimum number of colors.
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The maximum number of maximum generalized 4‐independent sets in trees
Journal of Graph TheoryAbstractA generalized ‐independent set is a set of vertices such that the induced subgraph contains no trees with ‐vertices, and the generalized ‐independence number is the cardinality of a maximum ‐independent set in . Zito proved that the maximum number of maximum generalized 2‐independent sets in a tree of order is if is odd, and if is even. Tu
Pingshan Li, Min Xu
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On Reducing Maximum Independent Set to Minimum Satisfiability
2014Maximum Independent Set (MIS) is a well-known NP-hard graph problem, tightly related with other well known NP-hard graph problems, namely Minimum Vertex Cover (MVC) and Maximum Clique (MaxClq). This paper introduces a novel reduction of MIS into Minimum Satisfiability (MinSAT), thus, providing an alternative approach for solving MIS.
Alexey Ignatiev +2 more
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On the maximum number of maximum independent sets in connected graphs
Journal of Graph Theory, 2021Dieter Rautenbach
exaly
Applications of maximum independent set
AIP Conference Proceedings, 2022Abbas Musleh Salman +1 more
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Polynomial-time Algorithm for Maximum Weight Independent Set on P 6 -free Graphs
ACM Transactions on Algorithms, 2022Marcin Pilipczuk +2 more
exaly
Critical and Maximum Independent Sets Revisited
2019Vadim E. Levit, Eugen Mandrescu
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A note on greedy algorithms for the maximum weighted independent set problem
Discrete Applied Mathematics, 2003Koichi Yamazaki, Shuichi Sakai
exaly
Using critical sets to solve the maximum independent set problem
Operations Research Letters, 2007Sergiy Butenko
exaly