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Extending the MAX Algorithm for Maximum Independent Set [PDF]
Discussiones Mathematicae Graph Theory, 2015 The maximum independent set problem is an NP-hard problem. In this paper, we consider Algorithm MAX, which is a polynomial time algorithm for finding a maximal independent set in a graph G.
Lê Ngoc C. +2 more
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Engineering Science and Technology, an International JournalIn this study, a method has been developed for solving the maximum independent set problem, which is one of the significant problems in graph theory. The maximum independent set problem is NP-hard for all types of graphs.
Furkan Öztemiz
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A reduction from an LWE problem to maximum independent set problems [PDF]
Scientific Reports, 2023 The learning with errors (LWE) problem is a problem derived from machine learning that is believed to be intractable for quantum computers. This paper proposes a method that can reduce an LWE problem to a set of maximum independent set (MIS) problems ...
Yasuhito Kawano
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Using synchronized oscillators to compute the maximum independent set [PDF]
Nature Communications, 2020 Designing efficient analog dynamical systems for solving hard optimization problems remains a challenge. Here, the authors demonstrate a dynamical system of thirty oscillators with reconfigurable coupling to compute optimal/near-optimal solutions to the ...
Antik Mallick +5 more
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Exact algorithms for maximum independent set [PDF]
Information and Computation, 2013 We show that the maximum independent set problem (MIS) on an $n$-vertex graph can be solved in $1.1996^nn^{O(1)}$ time and polynomial space, which even is faster than Robson's $1.2109^{n}n^{O(1)}$-time exponential-space algorithm published in 1986. We also obtain improved algorithms for MIS in graphs with maximum degree 6 and 7, which run in time of $1.
Mingyu Xiao 0001, Hiroshi Nagamochi
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On the Maximum Number of Maximum Independent Sets [PDF]
Graphs and Combinatorics, 2018 We give a very short and simple proof of Zykov's generalization of Turán's theorem, which implies that the number of maximum independent sets of a graph of order $n$ and independence number $α$ with $αn$, and we also characterize the extremal graphs.
Dieter Rautenbach
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Maximum independent set in multiplex social networks and its application to influence maximization [PDF]
Scientific ReportsIdentifying the most influential spreaders as an influence maximization problem (IMP) has become one of the most compelling topics in social network analysis due to its successes in viral marketing.
Mohammad Mehdi Daliri Khomami +2 more
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Quantum computing dataset of maximum independent set problem on king lattice of over hundred Rydberg atoms [PDF]
Scientific DataFinding the maximum independent set (MIS) of a large-size graph is a nondeterministic polynomial-time (NP)-complete problem not efficiently solvable with classical computations.
Kangheun Kim +4 more
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Critical sets, crowns and local maximum independent sets [PDF]
Journal of Global Optimization, 2021 A set $S\subseteq V(G)$ is independent (or stable) if no two vertices from $S$ are adjacent, and by $\mathrm{Ind}(G)$ we mean the set of all independent sets of $G$. A set $A\in\mathrm{Ind}(G)$ is critical (and we write $A\in CritIndep(G)$) if $\left\vert A\right\vert -\left\vert N(A)\right\vert =\max\{\left\vert I\right\vert -\left\vert N(I)\right ...
Vadim E. Levit, Eugen Mandrescu
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Critical and maximum independent sets of a graph [PDF]
Discrete Applied Mathematics, 2018 12 pages, 9 figures.
Adi Jarden +2 more
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