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All-Pairs Small-Stretch Paths (1997)
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| Venue: | Journal of Algorithms |
| Citations: | 37 - 7 self |
BibTeX
@ARTICLE{Cohen97all-pairssmall-stretch,
author = {Edith Cohen and Uri Zwick},
title = {All-Pairs Small-Stretch Paths},
journal = {Journal of Algorithms},
year = {1997},
volume = {38},
pages = {2001}
}
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Abstract
Let G = (V; E) be a weighted undirected graph. A path between u; v 2 V is said to be of stretch t if its length is at most t times the distance between u and v in the graph. We consider the problem of finding small-stretch paths between all pairs of vertices in the graph G. It is easy to see that finding paths of stretch less than 2 between all pairs of vertices in an undirected graph with n vertices is at least as hard as the Boolean multiplication of two n \Theta n matrices. We describe three algorithms for finding small-stretch paths between all pairs of vertices in a weighted graph with n vertices and m edges. The first algorithm, STRETCH 2 , runs in ~ O(n 3=2 m 1=2 ) time and finds stretch 2 paths. The second algorithm, STRETCH 7=3 , runs in ~ O(n 7=3 ) time and finds stretch 7/3 paths. Finally, the third algorithm, STRETCH 3 , runs in ~ O(n 2 ) and finds stretch 3 paths. Our algorithms are simpler, more efficient and more accurate than the previously best algorithms ...
