Results 1  10
of
799
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. ..."
Abstract

Cited by 99 (5 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 19 (1 self)
 Add to MetaCart
problem on trees can be approximated within a factor of 8 3 + ɛ, for any fixed ɛ> 0, and within O(log 2 n log log n) on general graphs, where n is the number of vertices in the graph. For any fixed ɛ> 0, we also obtain a polynomial time algorithm for kmulticut on trees which returns a solution
Approximating directed multicuts
, 2004
"... The Directed Multicut (DM) problem is: given a simple directed graph G = (V, E) with positive capacities ue on the edges, and a set K ⊆ V × V of ordered pairs of nodes of G, find a minimum capacity Kmulticut; C ⊆ E is a Kmulticut if in G − C there is no (s, t)path for every (s, t) ∈ K. In the un ..."
Abstract
 Add to MetaCart
. In the uncapacitated case (UDM) the goal is to find a minimum size Kmulticut. The best approximation ratio known for DM is min{O ( √ n), opt} by Anupam Gupta [G03], where n = V , and opt is the optimal solution value. All known nontrivial approximation algorithms for the problem solve large linear programs. We
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 ..."
Abstract

Cited by 103 (3 self)
 Add to MetaCart
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
Approximation Algorithms for Steiner and Directed Multicuts
 JOURNAL OF ALGORITHMS
, 1996
"... In this paper we consider the steiner multicut problem. This is a generalization of the minimum multicut problem where instead of separating node pairs, the goal is to find a minimum weight set of edges that separates all given sets of nodes. A set is considered separated if it is not contained in ..."
Abstract

Cited by 26 (1 self)
 Add to MetaCart
in a single connected component. We show an O(log 3 (kt)) approximation algorithm for the steiner multicut problem, where k is the number of sets and t is the maximum cardinality of a set. This improves the O(t log k) bound that easily follows from the previously known multicut results. We also
Abstract 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 ..."
Abstract
 Add to MetaCart
problem on trees can be approximated within a factor of 8 3 + ɛ, for any fixed ɛ> 0, and within O(log 2 nlog log n) on general graphs, where n is the number of vertices in the graph. For any fixed ɛ> 0, we also obtain a polynomial time algorithm for kmulticut on trees which returns a solution
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 ..."
Abstract

Cited by 20 (0 self)
 Add to MetaCart
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
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 ..."
Abstract

Cited by 8 (4 self)
 Add to MetaCart
of edges whose removal from T disconnects at least t out of these k pairs. This problem generalizes the wellknown multicut on a tree problem, in which we are required to disconnect all given pairs. The main contribution of this paper is an ( 8 + ɛ)approximation algo3 rithm for partial multicut on a tree
Results 1  10
of
799