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Iterative quantum algorithms for maximum independent set
Physical Review A, 2023Quantum algorithms have been widely studied in the context of combinatorial optimization problems. While this endeavor can often analytically and practically achieve quadratic speedups, theoretical and numeric studies remain limited, especially compared ...
L. Brady, Stuart Hadfield
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A 3-Approximation Algorithm for Maximum Independent Set of Rectangles
ACM-SIAM Symposium on Discrete Algorithms, 2022,
Waldo Gálvez +5 more
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Towards Computing a Near-Maximum Weighted Independent Set on Massive Graphs
Knowledge Discovery and Data Mining, 2021The vertices in many graphs are weighted unequally in real scenarios, but the previous studies on the maximum independent set (MIS) ignore the weights of vertices. Therefore, the weight of an MIS may not necessarily be the largest.
Jiewei Gu +3 more
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On Dominating Sets and Independent Sets of Graphs
Combinatorics, Probability and Computing, 1999For a graph G on vertex set V = {1, …, n} let k = (k1, …, kn) be an integral vector such that 1 [les ] ki [les ] di for i ∈ V, where di is the degree of the vertex i in G. A k-dominating set is a set Dk ⊆ V such that every vertex i ∈ V[setmn ]Dk has at least ki neighbours in Dk.
Jochen Harant +2 more
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Parameterized complexity of independent set reconfiguration problems
Discrete Applied Mathematics, 2020Suppose that we are given two independent sets I 0 and I r of a graph such that | I 0 | = | I r | , and imagine that a token is placed on each vertex in I 0 .
Takehiro Ito +5 more
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Combinatorica, 1990
A family of pairwise disjoint compact convex sets is called convexly independent, if none of its members is contained in the convex hull of the union of the other members of the family. The main result of the paper gives an upper bound for the maximum cardinalityh(k, n) of a family ℱ of mutually disjoint compact convex sets such that any subfamily of ...
Tibor Bisztriczky, Gábor Fejes Tóth
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A family of pairwise disjoint compact convex sets is called convexly independent, if none of its members is contained in the convex hull of the union of the other members of the family. The main result of the paper gives an upper bound for the maximum cardinalityh(k, n) of a family ℱ of mutually disjoint compact convex sets such that any subfamily of ...
Tibor Bisztriczky, Gábor Fejes Tóth
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Independent Gödel sentences and independent sets
Journal of Symbolic Logic, 1975In this paper we investigate some of the recursion-theoretic problems which are suggested by the logical notion of independence.A set S of natural numbers will be said to be k-independent (respectively, ∞-independent) if, roughly speaking, in every correct system there is a k-element set (respectively, an infinite set) of independent true sentences of ...
A. M. Dawes, John B. Florence
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2013
A set of edges in a graph G is independent if no two elements are contained in a clique of G. The edge-independent set problem asks for the maximal cardinality of independent sets of edges. We show that the edge-clique graphs of cocktail parties have unbounded rankwidth.
Ton Kloks +2 more
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A set of edges in a graph G is independent if no two elements are contained in a clique of G. The edge-independent set problem asks for the maximal cardinality of independent sets of edges. We show that the edge-clique graphs of cocktail parties have unbounded rankwidth.
Ton Kloks +2 more
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On covering an independent set in a grid with a second independent set
Journal of Graph Theory, 1996It is shown that for every independent set \(X\) in an \(n \times m\) grid, \(n,m>1\), there is a second independent set \(Y\) such that every member of \(X\) is adjacent to at least one member of \(Y\). The proof gives a construction of \(Y\). This is equivalent to showing that every maximal independent set in a grid has a second, disjoint, maximal ...
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A High-Quality and Fast Maximal Independent Set Implementation for GPUs
TOPC, 2019Computing a maximal independent set is an important step in many parallel graph algorithms. This article introduces ECL-MIS, a maximal independent set implementation that works well on GPUs.
Martin Burtscher +4 more
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