Techniques for the design of parallel graph algorithms
In this dissertation the author proposes some general algorithmic techniques to solve graph problems on parallel computers efficiently. He argues that the approach to solving graph problems in parallel should be to reduce them to other problems that have simple algorithms. While this approach is often implicit in current research, no special attention has been paid to the development of techniques particularly suited to carry out this reduction process. As a consequence, parallel graph algorithms resulting from the use of traditional techniques are either complicated or inefficient. To remedy this situation, he introduces two new techniques: the local replacement technique and the successive approximation technique. In support of the methodological point of view, he has used the local replacement technique to develop efficient parallel algorithms for two problems: the sparse, biconnected spanning subgraph problem, and the problem of testing of triconnectivity. In particular, the second algorithm, which is superior, to all existing ones can be used to (a) test a biconnected graph for triconnectivity, and (b) list the separating pairs of a biconnected graph in an encoded form when the graph is not triconnected. The model of computation assumed, for the most part, is CRCW PRAM. The broader question of the usefulness of the technique of local replacement in the design of algorithms on practical models, however, needs to be investigated more thoroughly. The second method, that of successive approximations, is used to find efficient implementations of graph algorithms on realistic models. He gives an implementation of an open ear decomposition algorithm using this technique. His implementation runs in O(log{sup 3}n) time on a mesh of trees of size O(n/log n {times} n/log n).
- Research Organization:
- Texas Univ., Austin, TX (United States)
- OSTI ID:
- 5856795
- Country of Publication:
- United States
- Language:
- English
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