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134,066
The Disjoint Paths Problem
, 1995
"... Introduction A basic problem that arises in largescale communication networks is that of assigning paths to connection requests. Each connection request is a pair of physically separated nodes that wish to communicate over a path through the network; given a list of such requests, one wants to ass ..."
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to assign paths to as many as possible in such a way that no two paths "interfere" with each other. Thus, for a given list of requests, we can ask a number of natural questions. How many requests are simultaneously realizable using paths that are mutually edgedisjoint? How many rounds
Disjoint Paths in Arborescences
, 2004
"... An arborescence in a digraph is a tree directed away from its root. A classical theorem of Edmonds characterizes which digraphs have λ arcdisjoint arborescences rooted at r. A similar theorem of Menger guarantees λ strongly arc disjoint rvpaths for every vertex v, where “strongly ” means no two pa ..."
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An arborescence in a digraph is a tree directed away from its root. A classical theorem of Edmonds characterizes which digraphs have λ arcdisjoint arborescences rooted at r. A similar theorem of Menger guarantees λ strongly arc disjoint rvpaths for every vertex v, where “strongly ” means no two
Computing Disjoint Paths on Polytopes
, 2005
"... Abstract The HoltKlee Condition states that there exist at least d vertexdisjoint strictly monotone pathsfrom the source to the sink of a polytopal digraph consisting of the set of vertices and arcs of a ..."
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Abstract The HoltKlee Condition states that there exist at least d vertexdisjoint strictly monotone pathsfrom the source to the sink of a polytopal digraph consisting of the set of vertices and arcs of a
Constrained Disjoint Paths in Geometric Network
"... We address the problem of constructing a pair of node disjoint paths connecting two given nodes in a geometric network. We propose a simple algorithm for constructing such a path that does not use any complicated data structure which can be implemented very easily. We also consider two variations of ..."
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We address the problem of constructing a pair of node disjoint paths connecting two given nodes in a geometric network. We propose a simple algorithm for constructing such a path that does not use any complicated data structure which can be implemented very easily. We also consider two variations
Kernel bounds for disjoint cycles and disjoint paths
, 2009
"... In this paper, we give evidence for the problems Disjoint Cycles and Disjoint Paths that they cannot be preprocessed in polynomial time such that resulting instances always have a size bounded by a polynomial in a specified parameter (or, in short: do not have a polynomial kernel); these results ..."
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Cited by 74 (16 self)
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In this paper, we give evidence for the problems Disjoint Cycles and Disjoint Paths that they cannot be preprocessed in polynomial time such that resulting instances always have a size bounded by a polynomial in a specified parameter (or, in short: do not have a polynomial kernel); these results
MaximumBandwidth NodeDisjoint Paths
"... Abstract—This paper presents a new method for finding the nodedisjoint paths with maximum combined bandwidth in communication networks. This problem is an NPcomplete problem which can be optimally solved in exponential time using integer linear programming (ILP). The presented method uses a maximu ..."
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Abstract—This paper presents a new method for finding the nodedisjoint paths with maximum combined bandwidth in communication networks. This problem is an NPcomplete problem which can be optimally solved in exponential time using integer linear programming (ILP). The presented method uses a
EdgeDisjoint Paths in Expander Graphs
, 2000
"... Given a graph G = (V, E) and a set of n pairs of vertices in V, we are interested in finding for each pair (ai, bi), a path connecting ai to bi, such that the set of n paths so found is edgedisjoint. (For arbitrary graphs the problem is AfPcomplete, although it is in 7 > if n is fixed.) We ..."
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Cited by 27 (0 self)
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Given a graph G = (V, E) and a set of n pairs of vertices in V, we are interested in finding for each pair (ai, bi), a path connecting ai to bi, such that the set of n paths so found is edgedisjoint. (For arbitrary graphs the problem is AfPcomplete, although it is in 7 > if n is fixed.) We
Results 11  20
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134,066