Results 1  10
of
24
Fixedparameter tractability of multicut parameterized by the size of the cutset
, 2011
"... Given an undirected graph G, a collection {(s1, t1),...,(sk, tk)} of pairs of vertices, and an integer p, the EDGE MULTICUT problem ask if there is a set S of at most p edges such that the removal of S disconnects every si from the corresponding ti. VERTEX MULTICUT is the analogous problem where S i ..."
Abstract

Cited by 32 (6 self)
 Add to MetaCart
Given an undirected graph G, a collection {(s1, t1),...,(sk, tk)} of pairs of vertices, and an integer p, the EDGE MULTICUT problem ask if there is a set S of at most p edges such that the removal of S disconnects every si from the corresponding ti. VERTEX MULTICUT is the analogous problem where S is a set of at most p vertices. Our main result is that both problems can be solved in time 2O(p3) · nO(1), i.e., fixedparameter tractable parameterized by the size p of the cutset in the solution. By contrast, it is unlikely that an algorithm with running time of the form f (p) · nO(1) exists for the directed version of the problem, as we show it to be W[1]hard parameterized by the size of the cutset.
Correlation clustering – minimizing disagreements on arbitrary weighted graphs
 Proceedings of the 11th Annual European Symposium on Algorithms
, 2003
"... ..."
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 ..."
Abstract

Cited by 14 (4 self)
 Add to MetaCart
(Show Context)
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 intensively studied for trees as well as for general graphs mainly from the viewpoint of polynomialtime approximation algorithms. By way of contrast, we provide a simple fixedparameter algorithm for Multicut in Trees showing
Complexity and Exact Algorithms for Vertex Multicut in Interval and Bounded Treewidth Graphs
, 2007
"... Multicut is a fundamental network communication and connectivity problem. It 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 w ..."
Abstract

Cited by 10 (0 self)
 Add to MetaCart
Multicut is a fundamental network communication and connectivity problem. It 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 the removal of terminal vertices. Complementing and refining previous results from the literature, we provide several NPcompleteness and (fixedparameter) tractability results for restricted classes of graphs such as trees, interval graphs, and graphs of bounded treewidth.
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 ..."
Abstract

Cited by 9 (1 self)
 Add to MetaCart
(Show Context)
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 the removal of terminal vertices. Complementing and refining previous results from the literature, we provide several NPcompleteness and (fixedparameter) tractability results for restricted classes of graphs such as trees, interval graphs, and graphs of bounded treewidth. 1
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 ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
(Show Context)
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 structure representing the graph and the set of pairs of terminal vertices as one such parameter. In this work, we show how this theoretical FPT result can be turned into efficient algorithms for optimization, counting, and enumeration problems in this area.
On the complexity of the multicut problem in bounded treewidth graphs and digraphs
, 2008
"... Given an edge or vertexweighted graph or digraph and a list of sourcesink pairs, the minimum multicut problem consists in selecting a minimum weight set of edges or vertices whose removal leaves no path from each source to the corresponding sink. This is a classical NPhard problem, and we show ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
Given an edge or vertexweighted graph or digraph and a list of sourcesink pairs, the minimum multicut problem consists in selecting a minimum weight set of edges or vertices whose removal leaves no path from each source to the corresponding sink. This is a classical NPhard problem, and we show that the edge version becomes tractable in bounded treewidth graphs if the number of sourcesink pairs is fixed, but remains NPhard in directed acyclic graphs and APXhard in bounded treewidth and bounded degree unweighted digraphs. The vertex version, although tractable in trees, is proved to be NPhard in unweighted cacti of bounded degree and bounded pathwidth.
DWidth Metric embeddings and their connections
, 2007
"... Embedding between metric spaces is a very powerful algorithmic tool and has been used for finding good approximation algorithms for several problems. In particular, embedding to an ℓ1 norm has been used as the key step in an approximation algorithm for the sparsest cut problem. The sparsest cut prob ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
(Show Context)
Embedding between metric spaces is a very powerful algorithmic tool and has been used for finding good approximation algorithms for several problems. In particular, embedding to an ℓ1 norm has been used as the key step in an approximation algorithm for the sparsest cut problem. The sparsest cut problem, in turn, is the main ingredient of many algorithms that have a divide and conquer nature and are used in various fields. While every metric is embeddable into ℓ1 with distortion O(log n) [13], and the bound is tight [39], for special classes of metrics better bounds exist. Shortest path metrics for trees and outerplanar graphs are isometrically embeddable into ℓ1 [41]. Seriesparallel graphs [28] and kouterplanar graphs [19](for constant k) are embeddable into ℓ1 with constant distortion, planar graphs and bounded treewidth graphs are conjectured to have constant distortion in embedding to ℓ1. Bounded treewidth graphs are one of most general graph classes on which several hard problems are tractable. We study the embedding of seriesparallel graphs (or, more generally, graphs
The parameterised complexity of list problems on graphs
, 2012
"... of bounded treewidth ..."
(Show Context)
Edge disjoint paths and multicut problems in graphs generalizing the trees
, 2005
"... We generalize all the results obtained for maximum integer multiflow and minimum multicut problems in trees by Garg et al. [Primaldual approximation algorithms for integral flow and multicut in trees. Algorithmica 18 (1997) 3–20] to graphs with a fixed cyclomatic number, while this cannot be achieve ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
We generalize all the results obtained for maximum integer multiflow and minimum multicut problems in trees by Garg et al. [Primaldual approximation algorithms for integral flow and multicut in trees. Algorithmica 18 (1997) 3–20] to graphs with a fixed cyclomatic number, while this cannot be achieved for other classical generalizations of the trees. Moreover, we prove that the minimum multicut problem with a fixed number of sourcesink pairs is polynomialtime solvable in planar and in bounded treewidth graphs. Eventually, we introduce the class of kedgeouterplanar graphs and show that the integrality gap of the maximum edgedisjoint paths problem is bounded in these graphs. We also provide stronger results for cacti (k = 1).