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Approximation algorithms for edgedisjoint paths and unsplittable flow
 Efficient Approximation and Online Algorithms
, 2006
"... Abstract. In the maximum edgedisjoint paths problem (MEDP) the input consists of a graph and a set of requests (pairs of vertices), and the goal is to connect as many requests as possible along edgedisjoint paths. We give a survey of known results about the complexity and approximability of MEDP ..."
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Abstract. In the maximum edgedisjoint paths problem (MEDP) the input consists of a graph and a set of requests (pairs of vertices), and the goal is to connect as many requests as possible along edgedisjoint paths. We give a survey of known results about the complexity and approximability of MEDP
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
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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present a polynomial time randomized algorithm for finding edge disjoint paths in an rregular expander graph G. We show that if G has sufficiently strong expansion properties and r is sufficiently large then all sets of n = f(n/log n) pairs of vertices can be joined. This is within a constant factor
Linear pattern matching algorithms
 IN PROCEEDINGS OF THE 14TH ANNUAL IEEE SYMPOSIUM ON SWITCHING AND AUTOMATA THEORY. IEEE
, 1972
"... In 1970, Knuth, Pratt, and Morris [1] showed how to do basic pattern matching in linear time. Related problems, such as those discussed in [4], have previously been solved by efficient but suboptimal algorithms. In this paper, we introduce an interesting data structure called a bitree. A linear ti ..."
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Cited by 549 (0 self)
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In 1970, Knuth, Pratt, and Morris [1] showed how to do basic pattern matching in linear time. Related problems, such as those discussed in [4], have previously been solved by efficient but suboptimal algorithms. In this paper, we introduce an interesting data structure called a bitree. A linear
Finding the k Shortest Paths
, 1997
"... We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph. Our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges, in time O(m + n log n + k). We can also find the k shortest pat ..."
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Cited by 401 (2 self)
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We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph. Our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges, in time O(m + n log n + k). We can also find the k shortest
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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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
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
Finding community structure in networks using the eigenvectors of matrices
, 2006
"... We consider the problem of detecting communities or modules in networks, groups of vertices with a higherthanaverage density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as “modularity ” over possible div ..."
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Cited by 500 (0 self)
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We consider the problem of detecting communities or modules in networks, groups of vertices with a higherthanaverage density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as “modularity ” over possible
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning
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