Short paths in expander graphs
- MIT, Cambridge, MA (United States)
- Cornell Univ., Ithaca, NY (United States)
Graph expansion has proved to be a powerful general tool for analyzing the behavior of routing algorithms and the interconnection 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, multicommodify 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 multicommodily flow problem with arbitrary demands on a bounded-degree expander, there is a (1 + {epsilon})-optimal solution using only flow paths of polylogarithmic length. It follows that the multicommodity flow algorithm of Awerbuch and Leighton runs in nearly linear time per commodity in expanders. Our analysis is based on establishing the following: given edge weights on an expander G, one can increase some of the weights very slightly so the resulting shortest-path metric is smooth - the min-weight path between any pair of nodes uses a polylogarithmic number of edges. (iii) Every bounded-degree expander on n nodes contains every graph with O(n/log{sup O(1)} n) nodes and edges as a minor.
- OSTI ID:
- 457640
- Report Number(s):
- CONF-961004-; CNN: Grant 92-00226; TRN: 97:001036-0011
- Resource Relation:
- Conference: 37. annual symposium on foundations of computer science, Burlington, VT (United States), 13-16 Oct 1996; Other Information: PBD: 1996; Related Information: Is Part Of Proceedings of the 37th annual symposium on foundations of computer science; PB: 656 p.
- Country of Publication:
- United States
- Language:
- English
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