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Fixedparameter tractability and data reduction for Multicut in Trees
 Networks
, 2005
"... We study an NPcomplete (and MaxSNPhard) communication problem on tree networks, the socalled Multicut in Trees: given an undirected tree and some pairs of nodes of the tree, find out whether there is a set of at most k tree edges whose removal separates all given pairs of nodes. Multicut has been ..."
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We study an NPcomplete (and MaxSNPhard) communication problem on tree networks, the socalled Multicut in Trees: given an undirected tree and some pairs of nodes of the tree, find out whether there is a set of at most k tree edges whose removal separates all given pairs of nodes. Multicut has
The Multicut Lemma
, 2002
"... of P and by the corresponding eigenvectors. Denote by 0 = 1 2 : : : n the eigenvalues of L and by u the corresponding eigenvectors. Then, i = 1 i (5) u (6) for all i = 1; : : : n. Note that this lemma ensures that the eigenvalues of P are always real and the eigenvectors line ..."
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of P and by the corresponding eigenvectors. Denote by 0 = 1 2 : : : n the eigenvalues of L and by u the corresponding eigenvectors. Then, i = 1 i (5) u (6) for all i = 1; : : : n. Note that this lemma ensures that the eigenvalues of P are always real and the eigenvectors lineraly independent. Lemma 4 (Lumpability) Let P be a matrix with rows and columns indexed by V that has independent eigenvectors. Let = (C 1 ; C 2 ; : : : C k ) be a partition of V . Then, P has K eigenvectors that are piecewise constant w.r.t. and correspond to nonzero eigenvalues if and only if the sums P ik = P ij are constant for all i 2 C l and all k; l = 1; : : : k and the matrix ^ P = [ P kl ] k;l=1;:::K (with ^ P kl = j2C k P ij ; i 2 C l ) is nonsingular. Lemma 5 (Relationship between P and ^ P ) Assume that the conditions of Lemma 4 hold. Let v and 1 = 1 2 : : : K be the piecewise constant eigenvectors of P and their eigenvalues. Denote by 1 = ^
Partial multicuts in trees
 In Proceedings of the 3rd International Workshop on Approximation and Online Algorithms
, 2005
"... Abstract. Let T = (V, E) be an undirected tree, in which each edge is associated with a nonnegative cost, and let {s1, t1},..., {sk, tk} be a collection of k distinct pairs of vertices. Given a requirement parameter t ≤ k, the partial multicut on a tree problem asks to find a minimum cost set of ed ..."
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Cited by 8 (4 self)
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collecting variant, in which we are not required to disconnect all pairs, but rather incur penalties for failing to do so. We provide a Lagrangian multiplier preserving algorithm for the latter problem, with an approximation factor of 2. Finally, we present a new 2approximation algorithm for multicut on a tree
Improved Results for Directed Multicut
"... Abstract We give a simple algorithm for the MINIMUM DIRECTED MULTICUT problem, and show that it gives an O( ..."
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Abstract We give a simple algorithm for the MINIMUM DIRECTED MULTICUT problem, and show that it gives an O(
MULTICUT AND INTEGRAL MULTIFLOW IN RINGS
"... Abstract. We show how to solve in polynomial time the multicut and the maximum integral multiflow problems in rings. For the latter problem we generalize an approach proposed by Sai Anand and Erlebach for special cases of the call control problem in ring networks. Moreover, we give lineartime proc ..."
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Abstract. We show how to solve in polynomial time the multicut and the maximum integral multiflow problems in rings. For the latter problem we generalize an approach proposed by Sai Anand and Erlebach for special cases of the call control problem in ring networks. Moreover, we give linear
On Reducing the Cut Ratio to the Multicut Problem
, 1993
"... We compare two multicommodity flow problems, the maximum sum of flow, and the maximum concurrent flow. We show that, for a given graph and a given set of k commodities with specified demands, if the minimum capacity of a multicut is approximated by the maximum sum of flow within a factor of alpha, f ..."
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Cited by 4 (0 self)
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We compare two multicommodity flow problems, the maximum sum of flow, and the maximum concurrent flow. We show that, for a given graph and a given set of k commodities with specified demands, if the minimum capacity of a multicut is approximated by the maximum sum of flow within a factor of alpha
Multicut Algorithms via Tree Decompositions
, 2010
"... Various forms of multicut problems are of great importance in the area of network design. In general, these problems are intractable. However, several parameters have been identified which lead to fixedparameter tractability (FPT). Recently, Gottlob and Lee have proposed the treewidth of the struc ..."
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Cited by 4 (0 self)
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Various forms of multicut problems are of great importance in the area of network design. In general, these problems are intractable. However, several parameters have been identified which lead to fixedparameter tractability (FPT). Recently, Gottlob and Lee have proposed the treewidth
Treewidth reduction for the parameterized Multicut problem
, 2010
"... The parameterized Multicut problem consists in deciding, given a graph, a set of requests (i.e. pairs of vertices) and an integer k, whether there exists a set of k edges which disconnects the two endpoints of each request. Determining whether Multicut is FixedParameter Tractable with respect to k ..."
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Cited by 1 (1 self)
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The parameterized Multicut problem consists in deciding, given a graph, a set of requests (i.e. pairs of vertices) and an integer k, whether there exists a set of k edges which disconnects the two endpoints of each request. Determining whether Multicut is FixedParameter Tractable with respect to k
Results 1  10
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858