DMCA
A shortest path algorithm for real-weighted undirected graphs (1985)
Cached
Download Links
| Venue: | in 13th ACMSIAM Symp. on Discrete Algs |
| Citations: | 16 - 4 self |
BibTeX
@ARTICLE{Pettie85ashortest,
author = {Seth Pettie and Vijaya Ramachandran},
title = {A shortest path algorithm for real-weighted undirected graphs},
journal = {in 13th ACMSIAM Symp. on Discrete Algs},
year = {1985},
volume = {34},
pages = {267--276}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
Abstract. We present a new scheme for computing shortest paths on real-weighted undirected graphs in the fundamental comparison-addition model. In an efficient preprocessing phase our algorithm creates a linear-size structure that facilitates single-source shortest path computations in O(m log α) time, where α = α(m, n) is the very slowly growing inverse-Ackermann function, m the number of edges, and n the number of vertices. As special cases our algorithm implies new bounds on both the all-pairs and single-source shortest paths problems. We solve the all-pairs problem in O(mnlog α(m, n)) time and, if the ratio between the maximum and minimum edge lengths is bounded by n (log n)O(1) , we can solve the single-source problem in O(m + nlog log n) time. Both these results are theoretical improvements over Dijkstra’s algorithm, which was the previous best for real weighted undirected graphs. Our algorithm takes the hierarchy-based approach invented by Thorup. Key words. single-source shortest paths, all-pairs shortest paths, undirected graphs, Dijkstra’s
Keyphrases
real-weighted undirected graph shortest path algorithm all-pairs shortest path new scheme real weighted undirected graph inverse-ackermann function special case theoretical improvement undirected graph single-source shortest path single-source shortest path computation all-pairs problem fundamental comparison-addition model nlog log single-source problem dijkstra algorithm efficient preprocessing phase algorithm implies new bound minimum edge length linear-size structure key word hierarchy-based approach single-source shortest path problem
