Results 1  10
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99,744
Shortest VertexDisjoint TwoFace Paths in Planar Graphs
, 2008
"... Let G be a directed planar graph of complexity n, each arc having a nonnegative length. Let s and t be two distinct faces of G; let s1,..., sk be vertices incident with s; let t1,..., tk be vertices incident with t. We give an algorithm to compute k pairwise vertexdisjoint paths connecting the pai ..."
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Cited by 1 (0 self)
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Let G be a directed planar graph of complexity n, each arc having a nonnegative length. Let s and t be two distinct faces of G; let s1,..., sk be vertices incident with s; let t1,..., tk be vertices incident with t. We give an algorithm to compute k pairwise vertexdisjoint paths connecting
Connecting obstacles in vertexdisjoint paths
 In 26th European Workshop Comp Geom
, 2010
"... Given a set of k disjoint convex polygonal obstacles inside a triangular container, we add straightline noncrossing edges such that each obstacle has three vertexdisjoint paths to the container. We prove combinatorial bounds on the minimum number of edges that are always sufficient and sometimes n ..."
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Cited by 2 (1 self)
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Given a set of k disjoint convex polygonal obstacles inside a triangular container, we add straightline noncrossing edges such that each obstacle has three vertexdisjoint paths to the container. We prove combinatorial bounds on the minimum number of edges that are always sufficient and sometimes
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
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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paths from a given source s to each vertex in the graph, in total time O(m + n log n +kn). We describe applications to dynamic programming problems including the knapsack problem, sequence alignment, maximum inscribed polygons, and genealogical relationship discovery.
LinearTime Algorithms for Disjoint TwoFace Paths Problems in Planar Graphs
, 1993
"... In this paper we present a lineartime algorithm for the vertexdisjoint TwoFace Paths Problem in planar graphs, i.e., the problem of finding k vertexdisjoint paths between pairs of terminals which lie on two face boundaries. The algorithm is based on the idea of finding rightmost paths with a ce ..."
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Cited by 1 (0 self)
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In this paper we present a lineartime algorithm for the vertexdisjoint TwoFace Paths Problem in planar graphs, i.e., the problem of finding k vertexdisjoint paths between pairs of terminals which lie on two face boundaries. The algorithm is based on the idea of finding rightmost paths with a
A Framework for Dynamic Graph Drawing
 CONGRESSUS NUMERANTIUM
, 1992
"... Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized as follows ..."
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Cited by 627 (44 self)
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as follows: ffl We devise a model for dynamic graph algorithms, based on performing queries and updates on an implicit representation of the drawing, and we show its applications. ffl We present several efficient dynamic drawing algorithms for trees, seriesparallel digraphs, planar stdigraphs, and planar
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
Faster ShortestPath Algorithms for Planar Graphs
 STOC 94
, 1994
"... We give a lineartime algorithm for singlesource shortest paths in planar graphs with nonnegative edgelengths. Our algorithm also yields a lineartime algorithm for maximum flow in a planar graph with the source and sink on the same face. The previous best algorithms for these problems required\O ..."
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Cited by 204 (17 self)
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We give a lineartime algorithm for singlesource shortest paths in planar graphs with nonnegative edgelengths. Our algorithm also yields a lineartime algorithm for maximum flow in a planar graph with the source and sink on the same face. The previous best algorithms for these problems required
Probabilistic Roadmaps for Path Planning in HighDimensional Configuration Spaces
 IEEE INTERNATIONAL CONFERENCE ON ROBOTICS AND AUTOMATION
, 1996
"... A new motion planning method for robots in static workspaces is presented. This method proceeds in two phases: a learning phase and a query phase. In the learning phase, a probabilistic roadmap is constructed and stored as a graph whose nodes correspond to collisionfree configurations and whose edg ..."
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Cited by 1276 (124 self)
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A new motion planning method for robots in static workspaces is presented. This method proceeds in two phases: a learning phase and a query phase. In the learning phase, a probabilistic roadmap is constructed and stored as a graph whose nodes correspond to collisionfree configurations and whose
Results 1  10
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99,744