Article

Faster Shortest-Path Algorithms for Planar Graphs

09/1996;
Source: CiteSeer

ABSTRACT We give a linear-time algorithm for single-source shortest paths in planar graphs with nonnegative edge-lengths. Our algorithm also yields a linear-time algorithm for maximum flow in a planar graph with the source and sink on the same face. For the case where negative edge-lengths 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. This algorithm can be used to obtain similar bounds for computing a feasible flow in a planar network, for finding a perfect matching in a planar bipartite graph, and for finding a maximum flow in a planar graph when the source and sink are not on the same face. We also give parallel and dynamic versions of these algorithms. 1 Introduction Computing shortest paths is a fundamental and ubiquitous problem in network analysis. Aside from the importance of this problem in its own right, often the problem arises in the solution of other problems (e.g. network flow and matching). In thi...

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Keywords

1 Introduction
 
absolute value
 
algorithms
 
dynamic versions
 
feasible flow
 
linear-time algorithm
 
maximum flow
 
negative edge-lengths
 
negative length
 
network analysis
 
network flow
 
nonnegative edge-lengths
 
planar bipartite graph
 
planar graph
 
planar graphs
 
planar network
 
shortest paths
 
similar bounds
 
single-source shortest paths
 
ubiquitous problem