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Short Paths in Expander Graphs (1996)
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| Venue: | In Proceedings of the 37th Annual Symposium on Foundations of Computer Science |
| Citations: | 44 - 1 self |
BibTeX
@INPROCEEDINGS{Kleinberg96shortpaths,
author = {Jon Kleinberg and Ronitt Rubinfeld},
title = {Short Paths in Expander Graphs},
booktitle = {In Proceedings of the 37th Annual Symposium on Foundations of Computer Science},
year = {1996},
pages = {86--95}
}
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Abstract
Graph expansion has proved to be a powerful general tool for analyzing the behavior of routing algorithms and the inter--connection networks on which they run. We develop new routing algorithms and structural results for bounded--degree expander graphs. Our results are unified by the fact that they are all based upon, and extend, a body of work asserting that expanders are rich in short, disjoint paths. In particular, our work has consequences for the disjoint paths problem, multicommodity flow, and graph minor containment. We show: (i) A greedy algorithm for approximating the maximum disjoint paths problem achieves a polylogarithmic approximation ratio in bounded--degree expanders. Although our algorithm is both deterministic and on-line, its performance guarantee is an improvement over previous bounds in expanders. (ii) For a multicommodity flow problem with arbitrary demands on a bounded--degree expander, there is a (1+ ")--optimal solution using only flow paths of polylogarithmi...
Keyphrases
short path expander graph optimal solution greedy algorithm disjoint path bounded degree expanders polylogarithmic approximation ratio bounded degree expander graph disjoint path problem arbitrary demand graph expansion performance guarantee structural result minor containment maximum disjoint path problem multicommodity flow previous bound flow path multicommodity flow problem bounded degree expander inter connection network powerful general tool
