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Multicut is FPT
 In STOC
, 2011
"... Let G = (V,E) be a graph on n vertices and R be a set of pairs of vertices in V called requests. A multicut is a subset F of E such that every request xy of R is separator by F, i.e.every xypath of G intersects F. We show that there exists an O(f(k)nc) algorithm which decides if there exists a mult ..."
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Let G = (V,E) be a graph on n vertices and R be a set of pairs of vertices in V called requests. A multicut is a subset F of E such that every request xy of R is separator by F, i.e.every xypath of G intersects F. We show that there exists an O(f(k)nc) algorithm which decides if there exists a
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 = ^
On the Hardness of Approximating Multicut and SparsestCut
 In Proceedings of the 20th Annual IEEE Conference on Computational Complexity
, 2005
"... We show that the MULTICUT, SPARSESTCUT, and MIN2CNF ≡ DELETION problems are NPhard to approximate within every constant factor, assuming the Unique Games Conjecture of Khot [STOC, 2002]. A quantitatively stronger version of the conjecture implies inapproximability factor of Ω(log log n). 1. ..."
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Cited by 102 (5 self)
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We show that the MULTICUT, SPARSESTCUT, and MIN2CNF ≡ DELETION problems are NPhard to approximate within every constant factor, assuming the Unique Games Conjecture of Khot [STOC, 2002]. A quantitatively stronger version of the conjecture implies inapproximability factor of Ω(log log n). 1.
Approximating the kMulticut Problem
"... We study the kmulticut problem: Given an edgeweighted undirected graph, a set of l pairs of vertices, and a target k ≤ l, find the minimum cost set of edges whose removal disconnects at least k pairs. This generalizes the well known multicut problem, where k = l. We show that the kmulticut problem ..."
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Cited by 20 (1 self)
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We study the kmulticut problem: Given an edgeweighted undirected graph, a set of l pairs of vertices, and a target k ≤ l, find the minimum cost set of edges whose removal disconnects at least k pairs. This generalizes the well known multicut problem, where k = l. We show that the kmulticut
Improved results for directed multicut
 In Proc. of SODA, 2003
, 2003
"... We give a simple algorithm for the MINIMUM DIRECTED MULTICUT problem, and show that it gives anapproximation. This improves on the previous approximation guarantee of ��of Cheriyan, Karloff and Rabani [1], which was obtained by a more sophisticated algorithm. 1 ..."
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We give a simple algorithm for the MINIMUM DIRECTED MULTICUT problem, and show that it gives anapproximation. This improves on the previous approximation guarantee of ��of Cheriyan, Karloff and Rabani [1], which was obtained by a more sophisticated algorithm. 1
Approximating Minimum Feedback Sets and Multicuts in Directed Graphs
 ALGORITHMICA
, 1998
"... This paper deals with approximating feedback sets in directed graphs. We consider two related problems: the weighted feedback vertex set (fvs) problem, and the weighted feedback edge set problem (fes). In the fvs (resp. fes) problem, one is given a directed graph with weights (each of which is at le ..."
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Cited by 106 (3 self)
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fractional solution of the problem at hand, and n is the number of vertices in the graph. We also define a multicut problem in a special type of directed networks which we call circular networks, and show that the subsetfes and subsetfvs problems are equivalent to this multicut problem. Another
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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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
Complexity and exact algorithms for multicut
 In: SOFSEM
"... Abstract. The Multicut problem is defined as: given an undirected graph and a collection of pairs of terminal vertices, find a minimum set of edges or vertices whose removal disconnects each pair. We mainly focus on the case of removing vertices, where we distinguish between allowing or disallowing ..."
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Abstract. The Multicut problem is defined as: given an undirected graph and a collection of pairs of terminal vertices, find a minimum set of edges or vertices whose removal disconnects each pair. We mainly focus on the case of removing vertices, where we distinguish between allowing or disallowing
Results 1  10
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