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Algorithms for Multicommodity Flows in Planar Graphs
, 1989
"... Abstract. This paper gives efficient algorithms for the multicommodity flow problem for two classes Ct2 and Co~ of planar undirected graphs. Every graph in Ct2 has two face boundaries B t and B 2 such that each of the sourcesink pairs lies on B 1 or B 2. On the other hand, every graph in Cot has a ..."
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Abstract. This paper gives efficient algorithms for the multicommodity flow problem for two classes Ct2 and Co~ of planar undirected graphs. Every graph in Ct2 has two face boundaries B t and B 2 such that each of the sourcesink pairs lies on B 1 or B 2. On the other hand, every graph in Cot has
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 200 (15 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
Maximum stflow in directed planar graphs via shortest paths
"... Abstract. Minimum cuts have been closely related to shortest paths in planar graphs via planar duality – so long as the graphs are undirected. Even maximum flows are closely related to shortest paths for the same reason – so long as the source and the sink are on a common face. In this paper, we giv ..."
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Cited by 2 (1 self)
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Abstract. Minimum cuts have been closely related to shortest paths in planar graphs via planar duality – so long as the graphs are undirected. Even maximum flows are closely related to shortest paths for the same reason – so long as the source and the sink are on a common face. In this paper, we
Maximum Flows and Parametric Shortest Paths in Planar Graphs
"... We observe that the classical maximum flow problem in any directed planar graph G can be reformulated as a parametric shortest path problem in the oriented dual graph G ∗. This reformulation immediately suggests an algorithm to compute maximum flows, which runs in O(n log n) time. As we continuously ..."
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Cited by 14 (1 self)
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We observe that the classical maximum flow problem in any directed planar graph G can be reformulated as a parametric shortest path problem in the oriented dual graph G ∗. This reformulation immediately suggests an algorithm to compute maximum flows, which runs in O(n log n) time. As we
Oracles for bounded length shortest paths in planar graphs
 ACM Trans. Algorithms
"... We present a new approach for answering short path queries in planar graphs. For any fixed constant k and a given unweighted planar graph G = (V, E) one can build in O(V ) time a data structure, which allows to check in O(1) time whether two given vertices are at distance at most k in G and if so ..."
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Cited by 4 (1 self)
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a shortest path between them is returned. Graph G can be undirected as well as directed. Our data structure works in fully dynamic environment. It can be updated in O(1) time after removing an edge or a vertex while updating after an edge insertion takes polylogarithmic amortized time. Besides
Multiplesource shortest paths in embedded graphs
, 2012
"... Let G be a directed graph with n vertices and nonnegative weights in its directed edges, embedded on a surface of genus g, and let f be an arbitrary face of G. We describe an algorithm to preprocess the graph in O(gn log n) time, so that the shortestpath distance from any vertex on the boundary of ..."
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Cited by 12 (6 self)
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of f to any other vertex in G can be retrieved in O(log n) time. Our result directly generalizes the O(n log n)time algorithm of Klein [Multiplesource shortest paths in planar graphs. In Proc. 16th Ann. ACMSIAM Symp. Discrete Algorithms, 2005] for multiplesource shortest paths in planar graphs
A Fully Dynamic Approximation Scheme for Shortest Paths in Planar Graphs
, 1998
"... In this paper we give a fully dynamic approximation scheme for maintaining allpairs shortest paths in planar networks. Given an error parameter ε such that 0 < ε, our algorithm maintains approximate allpairs shortest paths in an undirected planar graph G with nonnegative edge lengths. The appr ..."
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Cited by 24 (2 self)
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In this paper we give a fully dynamic approximation scheme for maintaining allpairs shortest paths in planar networks. Given an error parameter ε such that 0 < ε, our algorithm maintains approximate allpairs shortest paths in an undirected planar graph G with nonnegative edge lengths
A Linear Algorithm for Analysis of Minimum Spanning and Shortest Path Trees of Planar Graphs
 Algorithmica
, 1992
"... We give a linear time and space algorithm for analyzing trees in planar graphs. The algorithm can be used to analyze the sensitivity of a minimum spanning tree to changes in edge costs, to find its replacement edges, and to verify its minimality. It can also be used to analyze the sensitivity of a s ..."
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Cited by 16 (0 self)
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singlesource shortest path tree to changes in edge costs, and to analyze the sensitivity of a minimum cost network flow. The algorithm is simple and practical. It uses the properties of a planar embedding, combined with a heapordered queue data structure. Let G = (V; E) be a planar graph, either directed
Computing shortest paths in seriesparallel graphs . . .
, 2006
"... Seriesparallel graphs, which are built by repeatedly applying series or parallel composition operations to paths, play an important role in computer science as they model the flow of information in many types of programs. For directed seriesparallel graphs, we study the problem of finding a shorte ..."
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Cited by 2 (0 self)
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undirected graphs or tournament graphs, constructing some path between given vertices is possible in logarithmic space while constructing a shortest path is NLcomplete.
More compact oracles for approximate distances in undirected planar graphs
 In SODA ’13
, 2013
"... Distance oracles are data structures that provide fast (possibly approximate) answers to shortestpath and distance queries in graphs. The tradeoff between the space requirements and the query time of distance oracles is of particular interest and the main focus of this paper. In FOCS‘01, Thorup int ..."
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Cited by 4 (2 self)
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Distance oracles are data structures that provide fast (possibly approximate) answers to shortestpath and distance queries in graphs. The tradeoff between the space requirements and the query time of distance oracles is of particular interest and the main focus of this paper. In FOCS‘01, Thorup
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