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A simple parallel algorithm for the maximal independent set problem
 SIAM Journal on Computing
, 1986
"... Simple parallel algorithms for the maximal independent set (MIS) problem are presented. The first algorithm is a Monte Carlo algorithm with a very local property. The local property of this algorithm may make it a useful protocol design tool in distributed computing environments and artificial intel ..."
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Cited by 458 (10 self)
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Simple parallel algorithms for the maximal independent set (MIS) problem are presented. The first algorithm is a Monte Carlo algorithm with a very local property. The local property of this algorithm may make it a useful protocol design tool in distributed computing environments and artificial
ON GENERATING ALL MAXIMAL INDEPENDENT SETS
, 1988
"... We present an algorithm that generates all maximal independent sets of a graph in lexicographic order, with only polynomial delay between the output of two successive independent sets. We also show that there is no polynomialdelay algorithm for generating all maximal independent sets in reverse lex ..."
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Cited by 214 (0 self)
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We present an algorithm that generates all maximal independent sets of a graph in lexicographic order, with only polynomial delay between the output of two successive independent sets. We also show that there is no polynomialdelay algorithm for generating all maximal independent sets in reverse
On Markov chains for independent sets
 Journal of Algorithms
, 1997
"... Random independent sets in graphs arise, for example, in statistical physics, in the hardcore model of a gas. A new rapidly mixing Markov chain for independent sets is defined in this paper. We show that it is rapidly mixing for a wider range of values of the parameter than the LubyVigoda chain, ..."
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Cited by 83 (17 self)
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Random independent sets in graphs arise, for example, in statistical physics, in the hardcore model of a gas. A new rapidly mixing Markov chain for independent sets is defined in this paper. We show that it is rapidly mixing for a wider range of values of the parameter than the LubyVigoda chain
Independent Sets With Domination Constraints
, 1999
"... A #independent set S in a graph is parameterized by a set # of nonnegative integers that constrains how the independent set S can dominate the remaining vertices (#v ## S : N(v) # S # #.) For all values of #, we classify as either NPcomplete or polynomialtime solvable the problems of ..."
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Cited by 23 (8 self)
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A #independent set S in a graph is parameterized by a set # of nonnegative integers that constrains how the independent set S can dominate the remaining vertices (#v ## S : N(v) # S # #.) For all values of #, we classify as either NPcomplete or polynomialtime solvable the problems
Hypergraph independent sets
"... The study of extremal problems related to independent sets in hypergraphs is a problem that has generated much interest. While independent sets in graphs are defined as sets of vertices containing no edges, hypergraphs have different types of independent sets depending on the number of vertices from ..."
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The study of extremal problems related to independent sets in hypergraphs is a problem that has generated much interest. While independent sets in graphs are defined as sets of vertices containing no edges, hypergraphs have different types of independent sets depending on the number of vertices
On independent sets in random graphs
, 2011
"... The independence number of a sparse random graph G(n, m) of average degree d = 2m/n is wellknown to be α(G(n, m)) ∼ 2n ln(d)/d with high probability. Moreover, a trivial greedy algorithm w.h.p. finds an independent set of size (1 + o(1)) · n ln(d)/d, i.e., half the maximum size. Yet in spite of 3 ..."
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Cited by 12 (0 self)
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The independence number of a sparse random graph G(n, m) of average degree d = 2m/n is wellknown to be α(G(n, m)) ∼ 2n ln(d)/d with high probability. Moreover, a trivial greedy algorithm w.h.p. finds an independent set of size (1 + o(1)) · n ln(d)/d, i.e., half the maximum size. Yet in spite
The number of independent sets in the grid graph
 SIAM J. Discrete Math
, 1998
"... Abstract. If f(m,n) is the (vertex) independence number of the m × n grid graph, then we show that the double limit η = def limm,n→ ∞ f(m,n) 1 mn exists, thereby refining earlier results of Weber [2] and Engel [1]. We establish upper and lower bounds for η, and prove that 1.503047782... ≤ η ≤ 1.5035 ..."
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Cited by 101 (4 self)
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.5035148.... Numerical computations suggest that the true value of η (the “hard square constant”) is around 1.5030480824753323.. Key words. independent sets, grid graphs AMS subject classifications. 05A16, 05C50, 82B20 Let Gm,n be the m×n grid graph. That is, the vertices of Gm,n are the (m+1)(n+1) points (i, j) (0 ≤ i
ON INDEPENDENT SETS OF VERTICES IN GRAPHS
"... Abstract. Among the remarkable sets of vertices of a graph, the independent sets of vertices (acronym IS, other name is the internal stabile sets of vertices) are important, because using them we can solve many classification and counting problems: in chemistry, automobiles traffic, espionage, the ..."
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Abstract. Among the remarkable sets of vertices of a graph, the independent sets of vertices (acronym IS, other name is the internal stabile sets of vertices) are important, because using them we can solve many classification and counting problems: in chemistry, automobiles traffic, espionage
Independent Crossings and Independent Sets
, 2008
"... A cluster in a drawing of a graph in the plane is the set of four endpoints of the two edges involved in a crossing. A independent drawing is a drawing in which the clusters are pairwise disjoint. Albertson [1] asked for the maximum k such that every independent drawing with k crossings has an indep ..."
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A cluster in a drawing of a graph in the plane is the set of four endpoints of the two edges involved in a crossing. A independent drawing is a drawing in which the clusters are pairwise disjoint. Albertson [1] asked for the maximum k such that every independent drawing with k crossings has
Results 1  10
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3,346,658