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Minimum Bisection is fixed parameter tractable
 THE PROCEEDINGS OF STOC
, 2013
"... In the classic Minimum Bisection problem we are given as input a graph G and an integer k. The task is to determine whether there is a partition of V (G) into two parts A and B such that A  − B  ≤ 1 and there are at most k edges with one endpoint in A and the other in B. In this paper we giv ..."
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Cited by 5 (0 self)
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In the classic Minimum Bisection problem we are given as input a graph G and an integer k. The task is to determine whether there is a partition of V (G) into two parts A and B such that A  − B  ≤ 1 and there are at most k edges with one endpoint in A and the other in B. In this paper we
A Polylogarithmic Approximation of the Minimum Bisection
, 2001
"... A bisection of a graph with n vertices is a partition of its vertices into two sets, each of size n=2. The bisection cost is the number of edges connecting the two sets. ..."
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Cited by 82 (7 self)
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A bisection of a graph with n vertices is a partition of its vertices into two sets, each of size n=2. The bisection cost is the number of edges connecting the two sets.
History of the Minimum Bisection Problem 1 Applications through DivideandConquer: VLSI design, sparse matrix
"... History of the Minimum Bisection Problem ..."
Approximating the Minimum Bisection Size (Extended Abstract)
, 2000
"... A bisection of a graph with n vertices is a partition of its vertices into two sets, each of size n=2. The bisection size is the number of edges connecting the two sets. Finding the bisection of minimum size is NPhard. We present an algorithm that finds a bisection that is within O( p n log n ..."
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Cited by 3 (0 self)
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A bisection of a graph with n vertices is a partition of its vertices into two sets, each of size n=2. The bisection size is the number of edges connecting the two sets. Finding the bisection of minimum size is NPhard. We present an algorithm that finds a bisection that is within O( p n log
Minimum Bisection is NPhard on Unit Disk Graphs
"... Abstract. In this paper we prove that the MinBisection problem is NPhard on unit disk graphs, thus solving a longstanding open question. ..."
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Abstract. In this paper we prove that the MinBisection problem is NPhard on unit disk graphs, thus solving a longstanding open question.
Approximation Schemes for Metric Minimum Bisection and Partitioning
"... We design polynomial time approximation schemes (PTASs) for Metric MINBISECTION, i.e. dividing a given nite metric space into two halves so as to minimize the sum of distances across the cut. The method extends to partitioning problems with arbitrary size constraints. Our approximation schemes depe ..."
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We design polynomial time approximation schemes (PTASs) for Metric MINBISECTION, i.e. dividing a given nite metric space into two halves so as to minimize the sum of distances across the cut. The method extends to partitioning problems with arbitrary size constraints. Our approximation schemes depend on a hybrid placement method and on a new application of linearized quadratic programs.
Coping with NPhardness: Approximating minimum bisection and heuristics for maximum clique
, 2001
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BranchandCut for a Semidefinite Relaxation of Largescale Minimum Bisection Problems
, 2007
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An Exact Combinatorial Algorithm for Minimum Graph Bisection
 MATH. PROGRAM., SER. A MANUSCRIPT NO. (WILL BE INSERTED BY THE EDITOR)
"... We present a novel exact algorithm for the minimum graph bisection problem, whose goal is to partition a graph into two equallysized cells while minimizing the number of edges between them. Our algorithm is based on the branchandbound framework and, unlike most previous approaches, it is fully c ..."
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Cited by 1 (0 self)
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We present a novel exact algorithm for the minimum graph bisection problem, whose goal is to partition a graph into two equallysized cells while minimizing the number of edges between them. Our algorithm is based on the branchandbound framework and, unlike most previous approaches, it is fully
Nonpolyhedral Relaxations of GraphBisection Problems
, 1993
"... We study the problem of finding the minimum bisection of a graph into two parts of prescribed sizes. We formulate two lower bounds on the problem by relaxing node and edgeincidence vectors of cuts. We prove that both relaxations provide the same bound. The main fact we prove is that the duality be ..."
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Cited by 38 (8 self)
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We study the problem of finding the minimum bisection of a graph into two parts of prescribed sizes. We formulate two lower bounds on the problem by relaxing node and edgeincidence vectors of cuts. We prove that both relaxations provide the same bound. The main fact we prove is that the duality
Results 1  10
of
119