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Edgedisjoint paths in planar graphs with constant congestion
 IN PROCEEDINGS OF THE 38TH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING, 2006
, 2009
"... We study the maximum edgedisjoint paths problem in undirected planar graphs: given a graph G and node pairs (demands) s1t1, s2t2,..., sktk, the goal is to maximize the number of demands that can be connected (routed) by edgedisjoint paths. The natural multicommodity flow relaxation has an Ω ( √ ..."
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Cited by 14 (2 self)
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We study the maximum edgedisjoint paths problem in undirected planar graphs: given a graph G and node pairs (demands) s1t1, s2t2,..., sktk, the goal is to maximize the number of demands that can be connected (routed) by edgedisjoint paths. The natural multicommodity flow relaxation has an Ω
EdgeDisjoint Paths in Planar Graphs with Short Total Length
, 1996
"... The problem of finding edgedisjoint paths in a planar graph such that each path connects two specified vertices on the outer face of the graph is well studied. The "classical" Eulerian case introduced by Okamura and Seymour [7] is solvable in linear time [10]. So far, the length of the pa ..."
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Cited by 6 (1 self)
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The problem of finding edgedisjoint paths in a planar graph such that each path connects two specified vertices on the outer face of the graph is well studied. The "classical" Eulerian case introduced by Okamura and Seymour [7] is solvable in linear time [10]. So far, the length
Edgedisjoint Paths in Graphs on Surfaces
"... We present a survey of results on the edgedisjoint paths problem and relate this problem to the edgedisjoint homotopic path and the edgedisjoint homotopic cycle problem. The latter problem is: given a graph G =(V � E) embedded on a surface S and closed curves C1�:::�Ck on S, nd necessary and su c ..."
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We present a survey of results on the edgedisjoint paths problem and relate this problem to the edgedisjoint homotopic path and the edgedisjoint homotopic cycle problem. The latter problem is: given a graph G =(V � E) embedded on a surface S and closed curves C1�:::�Ck on S, nd necessary and su
EDGE–DISJOINT PATHS IN PERMUTATION GRAPHS
"... In this paper we consider the following problem. Given an undirected graph G = (V,E) and vertices s1, t1; s2, t2, the problem is to determine whether or not G admits two edge–disjoint paths P1 and P2 connecting s1 with t1 and s2 with t2, respectively. We give a linear (O(V + E)) algorithm to s ..."
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In this paper we consider the following problem. Given an undirected graph G = (V,E) and vertices s1, t1; s2, t2, the problem is to determine whether or not G admits two edge–disjoint paths P1 and P2 connecting s1 with t1 and s2 with t2, respectively. We give a linear (O(V + E)) algorithm
Wiring EdgeDisjoint Layouts
, 1996
"... We consider the wiring or layer assignment problem for edgedisjoint layouts. The wiring problem is well understood for the case that the underlying layout graph is a square grid (see [8]). In this paper, we introduce a more general approach to this problem. For an edgedisjoint layout in the plane ..."
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We consider the wiring or layer assignment problem for edgedisjoint layouts. The wiring problem is well understood for the case that the underlying layout graph is a square grid (see [8]). In this paper, we introduce a more general approach to this problem. For an edgedisjoint layout in the plane
Edgedisjoint st Paths on Probabilistic Graphs
"... For a probabilistic graph $(G=(V, E, s, t),p) $ , where $G $ is an undirected graph with specified source vertex $s $ and sink vertex $t(s\neq t) $ in which each edge has independent failure probability and each vertex is assumed to be failurefree, and $p=(p(e_{1}), \ldots, p(e_{E})) $ is a vecto ..."
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vector consisting of failure probabilities $p(e;)s $ of all edges $e_{i}s $ in $E $ , we consider the problem of computing the expected maximum number $\Gamma_{(G,p)} $ of edgedisjoint st paths. It has been known that this computing problem is NPhard even if $G $ is restricted to several classes like
The Maximum EdgeDisjoint Paths Problem In Bidirected Trees
 SIAM Journal on Discrete Mathematics
, 1998
"... . A bidirected tree is the directed graph obtained from an undirected tree by replacing each undirected edge by two directed edges with opposite directions. Given a set of directed paths in a bidirected tree, the goal of the maximum edgedisjoint paths problem is to select a maximumcardinality subse ..."
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Cited by 19 (4 self)
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. A bidirected tree is the directed graph obtained from an undirected tree by replacing each undirected edge by two directed edges with opposite directions. Given a set of directed paths in a bidirected tree, the goal of the maximum edgedisjoint paths problem is to select a maximumcardinality
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
Escaping a grid by edgedisjoint paths
 In Proc. of the eleventh annual ACMSIAM symposium on Discrete algorithms
, 2000
"... We study the edgedisjoint escape problem in grids. Given a set of n sources in a twodimensional grid, the problem is to connect all sources to the grid boundary using a set of n edgedisjoint paths. Different from the conventional approach, which reduces the problem to a network flow problem, we s ..."
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Cited by 4 (0 self)
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We study the edgedisjoint escape problem in grids. Given a set of n sources in a twodimensional grid, the problem is to connect all sources to the grid boundary using a set of n edgedisjoint paths. Different from the conventional approach, which reduces the problem to a network flow problem, we
A Separator Theorem for Planar Graphs
, 1977
"... Let G be any nvertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which ..."
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Cited by 465 (1 self)
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Let G be any nvertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which
Results 1  10
of
129,659