Fast parallel algorithms on a class of graph structures with applications in relational databases and computer networks
Thesis/Dissertation
·
OSTI ID:5900286
The quest for efficient parallel algorithms for graph related problems necessitates not only fast computational schemes but also requires insights into their inherent structures that lend themselves to elegant problem solving methods. Towards this objective efficient parallel algorithms on a class of hypergraphs called acyclic hypergraphs and directed hypergraphs are developed in this thesis. In this thesis, first, the author presents efficient parallel algorithms for the following problems on graphs. (1) Determining whether a graph is strongly chordal, ptolemaic, or a block graph. If the graph is strongly chordal, determine the strongly perfect vertex elimination ordering. (2) Determining the minimal set of edges needed to make an arbitrary graph strong chordal, ptolemaic, or a block graph. (3) Determining the minimum cardinality dominating set, connected dominating set, total dominating set, and the domatic number of a strongly chordal graph. Secondly, he shows that the query implication problem (Q{sub 1} {yields} Q{sub 2}) on two queries, which is to determine whether the data retrieved by query Q{sub 1} is always a subset of the data retrieved by query Q{sub 2}, is not even in NP and in fact complete in {Pi}{sub 2{sup p}}. Thirdly, he develops efficient parallel algorithms for manipulating directed hypergraphs H such as finding a directed path in H, closure of H, and minimum equivalent hypergraph of H. Finally, he also presents an efficient parallel algorithm for multidimensional range search.
- Research Organization:
- Louisiana State Univ., Baton Rouge, LA (United States)
- OSTI ID:
- 5900286
- Country of Publication:
- United States
- Language:
- English
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