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Maximum Cardinality Matching
, 2013
"... A matching in a graph G is a subset M of the edges of G such that no two share an endpoint. A matching has maximum cardinality if its cardinality is at least as large as that of any other matching. An oddset cover OSC of a graph G is a labeling of the nodes of G with integers such that every edge o ..."
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A matching in a graph G is a subset M of the edges of G such that no two share an endpoint. A matching has maximum cardinality if its cardinality is at least as large as that of any other matching. An oddset cover OSC of a graph G is a labeling of the nodes of G with integers such that every edge
Maximum cardinality matching by evolutionary algorithms
 Proc. of 2002 U.K. Workshop on Computational Intelligence (UKCI’02
, 2002
"... The analysis of time complexity of evolutionary algorithms has always focused on some artificial binary problems. This paper considers the average time complexity of an evolutionary algorithm for maximum cardinality matching in a graph. It is shown that the evolutionary algorithm can produce matchin ..."
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Cited by 2 (1 self)
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The analysis of time complexity of evolutionary algorithms has always focused on some artificial binary problems. This paper considers the average time complexity of an evolutionary algorithm for maximum cardinality matching in a graph. It is shown that the evolutionary algorithm can produce
Maximum cardinality matchings on . . .
, 2006
"... To understand the working principles of randomized search heuristics like evolutionary algorithms they are analyzed on optimization problems whose structure is wellstudied. The idea is to investigate when it is possible to simulate clever optimization techniques for combinatorial optimization probl ..."
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problems by random search. The maximum matching problem is well suited for this approach since long augmenting paths do not allow immediate improvements by local changes. It is known that randomized search heuristics like simulated annealing, the Metropolis algorithm, the (1+1) EA and randomized local
Maximum Cardinality Search
"... We present a new algorithm, called MCSM, for computing minimal triangulations of graphs. LexBFS, a seminal algorithm for recognizing chordal graphs, was the genesis for two other classical algorithms: LexM and MCS. LexM extends the fundamental concept used in LexBFS, resulting in an algorit ..."
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We present a new algorithm, called MCSM, for computing minimal triangulations of graphs. LexBFS, a seminal algorithm for recognizing chordal graphs, was the genesis for two other classical algorithms: LexM and MCS. LexM extends the fundamental concept used in LexBFS, resulting in an algorithm that also computes a minimal triangulation of an arbitrary graph. MCS simplified the fundamental concept used in LexBFS, resulting in a simpler algorithm for recognizing chordal graphs. The new simpler algorithm MCSM combines the extension of LexM with the simplification of MCS, achieving all the results of LexM in the same time complexity.
Approximation Schemes for Maximum Cardinality Matching
, 1995
"... Let G = (V; E) be an undirected graph. Given an odd number k = 2l + 1, a matching M is said to be koptimal if it does not admit an augmenting path of length less than or equal to k. We prove jM j jM 3 j(l+1)=(l+2), where M 3 is a maximum cardinality matching. If M is not already (k + 2)optima ..."
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Cited by 5 (0 self)
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Let G = (V; E) be an undirected graph. Given an odd number k = 2l + 1, a matching M is said to be koptimal if it does not admit an augmenting path of length less than or equal to k. We prove jM j jM 3 j(l+1)=(l+2), where M 3 is a maximum cardinality matching. If M is not already (k + 2
MAXIMUM CARDINALITIES FOR TOPOLOGIES ON FINITE SETS
"... If [n] represents the first n natural numbers, D. Stephen showed in [3] that no topology on [n] with the exception of the discrete topology has more than 3(2 n " ) elements and that this number is a maximum. In this article we show that, if k is a nonnegative integer and k < _ n, then no top ..."
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, then no topology on [n] with precisely n k open singletons has more than (1 + 2 k)2 n " k ~ 1 elements and that this number is attainable over such topologies for k < n. We also show that the topology on [n] with no open singletons and the maximum number of elements has cardinality 1 + 2 n_2. Recently, A
On the Maximum Cardinality Search Lower Bound for Treewidth
, 2004
"... The Maximum Cardinality Search algorithm visits the vertices of a graph in some order, such that at each step, an unvisited vertex that has the largest number of visited neighbors becomes visited. An MCSordering of a graph is an ordering of the vertices that can be generated by the Maximum Cardinal ..."
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Cited by 9 (5 self)
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The Maximum Cardinality Search algorithm visits the vertices of a graph in some order, such that at each step, an unvisited vertex that has the largest number of visited neighbors becomes visited. An MCSordering of a graph is an ordering of the vertices that can be generated by the Maximum
Edge Projection and the Maximum Cardinality Stable Set Problem
, 1996
"... . Edge projection is a specialization of Lov'asz and Plummer's clique projection when restricted to edges. We discuss some properties of the edge projection which are then exploited to develop a new upper bound procedure for the Maximum Cardinality Stable Set Problem (MSS Problem). The upp ..."
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Cited by 11 (1 self)
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. Edge projection is a specialization of Lov'asz and Plummer's clique projection when restricted to edges. We discuss some properties of the edge projection which are then exploited to develop a new upper bound procedure for the Maximum Cardinality Stable Set Problem (MSS Problem
Computing MaximumCardinality Matchings in Sparse General Graphs
, 1998
"... We give an experimental study of a new O(mn ff(m; n)) time implementation of Edmonds' algorithm for a maximumcardinality matching in a sparse general graph of n vertices and m edges. The implementation incorporates several optimizations stemming from choosing a depthfirst order in which to ex ..."
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We give an experimental study of a new O(mn ff(m; n)) time implementation of Edmonds' algorithm for a maximumcardinality matching in a sparse general graph of n vertices and m edges. The implementation incorporates several optimizations stemming from choosing a depthfirst order in which
Maximum Cardinality Search for Computing Minimal Triangulations of Graphs
 ALGORITHMICA
, 2002
"... We present a new algorithm, called MCSM, for computing minimal triangulations of graphs. LexBFS, a seminal algorithm for recognizing chordal graphs, was the genesis for two other classical algorithms: LEX M and MCS. LEX M extends the fundamental concept used in LexBFS, resulting in an algorit ..."
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Cited by 45 (19 self)
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We present a new algorithm, called MCSM, for computing minimal triangulations of graphs. LexBFS, a seminal algorithm for recognizing chordal graphs, was the genesis for two other classical algorithms: LEX M and MCS. LEX M extends the fundamental concept used in LexBFS, resulting in an algorithm that not only recognizes chordality, but also computes a minimal triangulation of an arbitrary graph. MCS
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