Sequential and parallel algorithms on compactly represented chordal and strongly chordal graphs
For a given ordered graph (G, <), we consider the smallest (strongly) chordal graph G′ containing G with < as a (strongly) perfect elimination ordering. We call (G, <) a compact representation of G′. We show that the computation of a depth-first search tree and a breadth-first search tree can be done in polylogarithmic time with a linear processor number with respect to the size of the compact representation in parallel. We consider also the problems to find a maximum clique and to develop a data structure extension that allows an adjacency query in polylogarithmic time.
KeywordsAlgorithms and Data Structures Parallel Algorithms
Unable to display preview. Download preview PDF.
- 4.E. Dahlhaus, Fast parallel algorithm for the single link heuristics of hierarchical clustering, Proceedings of the fourth IEEE Symposium on Parallel and Distributed Processing (1992), pp. 184–186.Google Scholar
- 7.E. Dahlhaus, Efficient Parallel Algorithms on Chordal Graphs with a Sparse Tree Representation, Proceedings of the 27-th Annual Hawaii International Conference on System Sciences, Vol. II (1994), pp. 150–158.Google Scholar
- 13.J. Gilbert, H. Hafsteinsson, Parallel Solution of Sparse Linear Systems, SWAT 88 (1988), LNCS 318, pp. 145–153.Google Scholar
- 14.P. Klein, Efficient Parallel Algorithms for Chordal Graphs, 29. IEEE-FOCS (1988), pp. 150–161.Google Scholar
- 19.K. White, M. Farber, W. Pulleyblank, Steiner Trees, Connected Domination, and Strongly Chordal Graphs, Networks 15 (1985), pp. 109–124.Google Scholar