Results 1 
5 of
5
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 ..."
Abstract

Cited by 163 (13 self)
 Add to MetaCart
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\Omega\Gamma n p log n) time where n is the number of nodes in the input graph. For the case where negative edgelengths are allowed, we give an algorithm requiring O(n 4=3 log nL) time, where L is the absolute value of the most negative length. Previous algorithms for shortest paths with negative edgelengths required \Omega\Gamma n 3=2 ) time. Our shortestpath algorithm yields an O(n 4=3 log n)time algorithm for finding a perfect matching in a planar bipartite graph. A similar improvement is obtained for maximum flow in a directed planar graph.
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 ..."
Abstract

Cited by 140 (0 self)
 Add to MetaCart
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 which very little is known from the point of view of approximation algorithms. It has recently been brought into focus in work on problems such as VLSI layout and routing in highspeed networks; in these settings, the current lack of understanding of the disjoint paths problem is often an obstacle to the design of practical heuristics.
A LinearProcessor PolylogTime Algorithm for Shortest Paths in Planar Graphs
, 1993
"... We give an algorithm requiring polylog time and a linear number of processors to solve singlesource shortest paths in directed planar graphs, boundedgenus graphs, and 2dimensional overlap graphs. More generally, the algorithm works for any graph provided with a decomposition tree constructed using ..."
Abstract

Cited by 16 (5 self)
 Add to MetaCart
We give an algorithm requiring polylog time and a linear number of processors to solve singlesource shortest paths in directed planar graphs, boundedgenus graphs, and 2dimensional overlap graphs. More generally, the algorithm works for any graph provided with a decomposition tree constructed using sizeO( p n polylog n) separators.
Faster ShortestPath Algorithms for Planar Graphs
 Journal of Computer and System Sciences
, 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\Om ..."
Abstract
 Add to MetaCart
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\Omega\Gamma n p log n) time where n is the number of nodes in the input graph. For the case where negative edgelengths are allowed, we give an algorithm requiring O(n 4=3 log nL) time, where L is the absolute value of the most negative length. Previous algorithms for shortest paths with negative edgelengths required \Omega\Gamma n 3=2 ) time. Our shortestpath algorithm yields an O(n 4=3 log n)time algorithm for finding a perfect matching in a planar bipartite graph. A similar improvement is obtained for maximum flow in a directed planar graph. 1 Introduction Computing shortest paths is a fundamental and ubiquitous problem in network analysis. Aside from the importance of this p...