Results 21 to 30 of about 996,556 (196)
Scalable Kernelization for Maximum Independent Sets [PDF]
ACM Journal of Experimental Algorithmics, 2018 The most efficient algorithms for finding maximum independent sets in both theory and practice use reduction rules to obtain a much smaller problem instance called a kernel . The kernel can then be solved quickly using exact or heuristic algorithms—or by repeatedly kernelizing recursively in the branch-and-reduce ...
Demian Hespe +2 more
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Determination of the Maximum Set Independent Simple Paths between the Vertices of the Graph
Современные информационные технологии и IT-образование, 2021 This article presents an algorithm for determining the maximum number of independent simple paths, as well as the paths themselves, between the given vertices of the graph.
Yulia Terentyeva
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On the maximum number of maximum independent sets in connected graphs [PDF]
Journal of Graph Theory, 2020 AbstractWe characterize the connected graphs of given order and given independence number that maximize the number of maximum independent sets. For , there is a unique such graph that arises from the disjoint union of cliques of orders and , which is the complement of a Turán graph, by selecting a vertex in a largest clique and adding an edge ...
Elena Mohr, Dieter Rautenbach
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Maximum Weighted Independent Sets with a Budget [PDF]
, 2017 12 ...
Tushar Kalra +3 more
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Solving Robust Variants of the Maximum Weighted Independent Set Problem on Trees
Mathematics, 2020 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.
Ana Klobučar, Robert Manger
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Independent sets of maximum weight in apple-free graphs [PDF]
, 2010 We present the first polynomial-time algorithm to solve the maximum weight independent set problem for apple-free graphs, which is a common generalization of several important classes where the problem can be solved efficiently, such as claw-free graphs,
Lozin, Vadim V. +2 more
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On the maximum number of maximum independent sets of bipartite graphs
Mediterranean Journal of Mathematics, 2023 Abstract An independent set in a graph G is a set of pairwise non-adjacent vertices of G. The independence number, α, of G is the maximum cardinality of an independent set in G. An independent set in G is maximum if it has cardinality α. Mohr and Rautenbach determined the n-vertex trees (resp.
Sun, Wanting, Li, Shuchao
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Large neighborhood local search for the maximum set packing problem [PDF]
, 2013 In this paper we consider the classical maximum set packing problem where set cardinality is upper bounded by a constant k. We show how to design a variant of a polynomial-time local search algorithm with performance guarantee (k + 2)/3.
Sviridenko, Maxim +3 more
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An evolutionary algorithm for the robust maximum weighted independent set problem
Automatika, 2020 This work deals with the robust maximum weighted independent set problem, i.e. finding a subset of graph vertices that are not adjacent to each other and whose sum of weights is as large as possible.
Ana Klobučar, Robert Manger
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Coloring and Maximum Weight Independent Set of Rectangles [PDF]
, 2021 In 1960, Asplund and Grünbaum proved that every intersection graph of axis-parallel rectangles in the plane admits an $O(ω^2)$-coloring, where $ω$ is the maximum size of a clique. We present the first asymptotic improvement over this six-decade-old bound, proving that every such graph is $O(ω\logω)$-colorable and presenting a polynomial-time algorithm ...
Chalermsook, Parinya, Walczak, Bartosz
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