Results 1 
1 of
1
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 approxi ..."
Abstract

Cited by 17 (1 self)
 Add to MetaCart
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 approximate paths are guaranteed to be accurate to within a 1 + ε factor. The time bounds for both query and update for our algorithm is O(ε−1n2/3 log2 n log D), where n is the number of nodes in G and D is the sum of its edge lengths. The time bound for the queries is worst case, while that for the additions is amortized. Our approximation algorithm is based upon a novel technique for approximately representing allpairs shortest paths among a selected subset of the nodes by a sparse substitute graph.