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On a bidirected relaxation for the Multiway Cut problem
, 2005
"... Abstract In the Multiway Cut problem, we are given an undirected edgeweighted graph G = (V; E) with ce denoting the cost (weight) of edge e. We are also given a subset S of V, of size k, called the terminals. The objective is to find a minimum cost set of edges whose removal ensures that the termin ..."
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Abstract In the Multiway Cut problem, we are given an undirected edgeweighted graph G = (V; E) with ce denoting the cost (weight) of edge e. We are also given a subset S of V, of size k, called the terminals. The objective is to find a minimum cost set of edges whose removal ensures
MultiMultiway Cut Problem on Graphs of Bounded Branch Width
"... Abstract. The MultiMultiway Cut problem proposed by Avidor and Langberg[2] is a natural generalization of Multicut and Multiway Cut problems. That is, given a simple graphG and c sets of vertices S1, · · · , Sc, the problem asks for a minimum set of edges whose removal disconnects every pair of ..."
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Abstract. The MultiMultiway Cut problem proposed by Avidor and Langberg[2] is a natural generalization of Multicut and Multiway Cut problems. That is, given a simple graphG and c sets of vertices S1, · · · , Sc, the problem asks for a minimum set of edges whose removal disconnects every pair
Simplex Partitioning via Exponential Clocks and the Multiway Cut Problem (Extended Abstract)
, 2013
"... The MultiwayCut problem is a fundamental graph partitioning problem in which the objective is to find a minimum weight set of edges disconnecting a given set of special vertices called terminals. This problem is NPhard and there is a well known geometric relaxation in which the graph is embedded i ..."
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Cited by 7 (0 self)
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The MultiwayCut problem is a fundamental graph partitioning problem in which the objective is to find a minimum weight set of edges disconnecting a given set of special vertices called terminals. This problem is NPhard and there is a well known geometric relaxation in which the graph is embedded
Multiway cuts in node weighted graphs
 JOURNAL OF ALGORITHMS
, 2004
"... A (2 — 2/k) approximation algorithm is presented for the node multiway cut problem, thus matching the result of Dahlhaus et al. (SIAM J. Comput. 23 (4) (1994) 864894) for the edge version of this problem. This is done by showing that the associated LPrelaxation always has a halfintegral optimal s ..."
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Cited by 19 (0 self)
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A (2 — 2/k) approximation algorithm is presented for the node multiway cut problem, thus matching the result of Dahlhaus et al. (SIAM J. Comput. 23 (4) (1994) 864894) for the edge version of this problem. This is done by showing that the associated LPrelaxation always has a halfintegral optimal
On weighted multiway cuts in trees
 MATHEMATICAL PROGRAMMING
, 1994
"... A minmax theorem is developed for the multiway cut problem of edgeweighted trees. We present a polynomial time algorithm to construct an optimal dual solution, if edge weights come in unary representation. Applications to biology also require some more complex edge weights. We describe a dynarnic ..."
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Cited by 14 (0 self)
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A minmax theorem is developed for the multiway cut problem of edgeweighted trees. We present a polynomial time algorithm to construct an optimal dual solution, if edge weights come in unary representation. Applications to biology also require some more complex edge weights. We describe a dynarnic
1 LP for Multiway cut [1]
"... Last time we set up the following LP for the Multiway cut problem: uv xu − xv 1 · cuv min 1 2 s.t. xi = ei ∑ ∀terminal i j xuj =1 ∀u xu ≥ 0 ..."
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Last time we set up the following LP for the Multiway cut problem: uv xu − xv 1 · cuv min 1 2 s.t. xi = ei ∑ ∀terminal i j xuj =1 ∀u xu ≥ 0
Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming
 Journal of the ACM
, 1995
"... We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution ..."
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Cited by 1231 (13 self)
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We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds
"GrabCut”  interactive foreground extraction using iterated graph cuts
 ACM TRANS. GRAPH
, 2004
"... The problem of efficient, interactive foreground/background segmentation in still images is of great practical importance in image editing. Classical image segmentation tools use either texture (colour) information, e.g. Magic Wand, or edge (contrast) information, e.g. Intelligent Scissors. Recently ..."
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Cited by 1140 (36 self)
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The problem of efficient, interactive foreground/background segmentation in still images is of great practical importance in image editing. Classical image segmentation tools use either texture (colour) information, e.g. Magic Wand, or edge (contrast) information, e.g. Intelligent Scissors
Fast approximate energy minimization via graph cuts
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2001
"... In this paper we address the problem of minimizing a large class of energy functions that occur in early vision. The major restriction is that the energy function’s smoothness term must only involve pairs of pixels. We propose two algorithms that use graph cuts to compute a local minimum even when v ..."
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Cited by 2127 (61 self)
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In this paper we address the problem of minimizing a large class of energy functions that occur in early vision. The major restriction is that the energy function’s smoothness term must only involve pairs of pixels. We propose two algorithms that use graph cuts to compute a local minimum even when
Analysis of LP relaxations for multiway and multicut problems
 M.C. COSTA ET AL. / EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
, 1999
"... We introduce in this paper an exact nonlinear formulation of the multiway cut problem. By simple linearizations of this formulation, we derive several wellknown and new formulations for the problem. We further establish a connection between the multiway cut and the maximumweighted independent set ..."
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Cited by 2 (0 self)
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We introduce in this paper an exact nonlinear formulation of the multiway cut problem. By simple linearizations of this formulation, we derive several wellknown and new formulations for the problem. We further establish a connection between the multiway cut and the maximumweighted independent
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