Graduation Year

2005

Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Science

Department

Mathematics

Reader 1

Ran Libeskind-Hadas (CS)

Reader 2

Francis Edward Su

Abstract

The problem of edge disjoint path routing arises from applications in distributed memory parallel computing. We examine this problem in both the directed hypercube and two-dimensional grid topologies. Complexity results are obtained for these problems where the routing must consist entirely of shortest length paths. Additionally, approximation algorithms are presented for the case when the routing request is of a special form known as a permutation. Permutations simply require that no vertex in the graph may be used more than once as either a source or target for a routing request. Szymanski conjectured that permutations are always routable in the directed hypercube, and this remains an open problem.

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