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Approximation Algorithms for Disjoint Paths Problems
, 1996
"... The construction of disjoint paths in a network is a basic issue in combinatorial optimization: given a network, and specified pairs of nodes in it, we are interested in finding disjoint paths between as many of these pairs as possible. This leads to a variety of classical NPcomplete problems for w ..."
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Cited by 166 (0 self)
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The construction of disjoint paths in a network is a basic issue in combinatorial optimization: given a network, and specified pairs of nodes in it, we are interested in finding disjoint paths between as many of these pairs as possible. This leads to a variety of classical NPcomplete problems
Split Multipath Routing with Maximally Disjoint Paths in Ad Hoc Networks
 In Proc. Int. IEEE Conf. on Comm., 2001
"... Abstract – In recent years, routing has been the most focused area in ad hoc networks research. Ondemand routing in particular, is widely developed in bandwidth constrained mobile wireless ad hoc networks because of its effectiveness and efficiency. Most proposed ondemand routing protocols however ..."
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Cited by 435 (4 self)
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linkstate or distance vector algorithms which are not wellsuited for ad hoc networks. We propose an ondemand routing scheme called Split Multipath Routing (SMR) that establishes and utilizes multiple routes of maximally disjoint paths. Providing multiple routes helps minimizing route recovery
Planar disjointpaths completion
, 2011
"... We introduce Planar Disjoint Paths Completion, a completion counterpart of the Disjoint Paths problem, and study its parameterized complexity. The problem can be stated as follows: given a plane graph G, k pairs of terminals, and a face F of G, find a minimumsize set of edges, if one exists, to be ..."
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Cited by 3 (3 self)
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We introduce Planar Disjoint Paths Completion, a completion counterpart of the Disjoint Paths problem, and study its parameterized complexity. The problem can be stated as follows: given a plane graph G, k pairs of terminals, and a face F of G, find a minimumsize set of edges, if one exists
Maximum Flows on Disjoint Paths
, 2010
"... Abstract. We consider the question: What is the maximum flow achievable in a network if the flow must be decomposable into a collection of edgedisjoint paths? Equivalently, we wish to find a maximum weighted packing of disjoint paths, where the weight of a path is the minimum capacity of an edge on ..."
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Abstract. We consider the question: What is the maximum flow achievable in a network if the flow must be decomposable into a collection of edgedisjoint paths? Equivalently, we wish to find a maximum weighted packing of disjoint paths, where the weight of a path is the minimum capacity of an edge
Edge Disjoint Paths Revisited
 In Proceedings of the 14th ACMSIAM Symposium on Discrete Algorithms
, 2003
"... The approximability of the maximum edge disjoint paths problem (EDP) in directed graphs was seemingly settled by the )hardness result of Guruswami et al. [10] and the O( m) approximation achievable via both the natural LP relaxation [19] and the greedy algorithm [11, 12]. Here m is the numb ..."
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Cited by 40 (4 self)
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The approximability of the maximum edge disjoint paths problem (EDP) in directed graphs was seemingly settled by the )hardness result of Guruswami et al. [10] and the O( m) approximation achievable via both the natural LP relaxation [19] and the greedy algorithm [11, 12]. Here m
Disjoint Paths in Metacube
"... A new interconnection network with lowdegree for very large parallel computers called metacube (MC) has been introduced recently. The MC network has short diameter similar to that of the hypercube. However, the degree of an MC network is much lower than that of a hypercube of the same size. More th ..."
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(classcubes) and m is the dimension of the lowlevel cubes (clusters). In this paper, we describe an efficient algorithm for finding disjoint paths in MC networks. We show that, for any two distinct nodes u and v in an MC(k,m), k + m disjoint paths from u to v can be found in O(log 2 p) time. The length
Constructing Node (Edge) Disjoint Paths on the
"... In a (d, k)graph problem, the Petersen graph has a maximum of 10 nodes at degree 3 and diameter 2. Using the Petersen graph, a folded Petersen cube network, a hyperPetersen network, a cubeconnected Petersen network, a cyclic Petersen network, a Petersentorus network and a 3D PetersenTorus netwo ..."
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Torus network have been suggested. In an interconnection network, a disjoint path is an important research topic for efficient and reliable routing. In this study, a disjoint path on the Petersen graph was analyzed so that it could be applied to construction of a disjoint path in a network to be made using
Disjoint Paths in Densely Embedded Graphs
 in Proceedings of the 36th Annual Symposium on Foundations of Computer Science
, 1995
"... We consider the following maximum disjoint paths problem (mdpp). We are given a large network, and pairs of nodes that wish to communicate over paths through the network  the goal is to simultaneously connect as many of these pairs as possible in such a way that no two communication paths share a ..."
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Cited by 63 (6 self)
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We consider the following maximum disjoint paths problem (mdpp). We are given a large network, and pairs of nodes that wish to communicate over paths through the network  the goal is to simultaneously connect as many of these pairs as possible in such a way that no two communication paths share
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