Clustering bipartite and chordal graphs: Complexity, sequential and parallel algorithms

Discrete Applied Mathematics

Volumn 91, Issue 1-3, 1999, Pages 1-23

  Abbas, Nesrine ^a   Stewart, Lorna ^a  

^a UNIVERSITY OF ALBERTA   (Canada)

Author keywords

Algorithms; Bipartite graphs; Bipartite permutation graphs; Chordal graphs; Graph partitioning; Interval graphs

Indexed keywords

EID: 0141528808     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-218X(98)00094-8     Document Type: Article

References (26)

1. N. Abbas, Graph clustering: complexity, sequential and parallel algorithms, Ph.D. Thesis, Dept. of Computing Science, University of Alberta, 1995.
2. N. Abbas, L. Stewart, Partitioning vertices of chordal graphs, Congr. Numer. 93 (1993) 7-16.
3. S.G. Akl, The Design and Analysis of Parallel Algorithms, Prentice-Hall, Englewood Cliffs, NJ, 1989.
4. A.A. Bertossi, M.A. Bonuccelli, Some parallel algorithms on interval graphs, Discrete Appl. Math. 16 (1987) 101-111.
5. K.S. Booth, G.S. Lueker, Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms, J. Comput. Systems Sci. 13 (1976) 335-379.
6. E. Dekel, S. Sahni, A parallel matching algorithm for convex bipartite graphs and applications to scheduling, J. Parallel Distributed Comput. (1) (1984) 185-205.
7. J.S. Deogun, D. Kratsch, Diametral path graphs, Proc. WG'95, Lecture Notes in Mathematics, vol. 1017, Springer, Berlin, 1995, pp. 344-357.
8. J.S. Deogun, D. Kratsch, G. Steiner, An approximation algorithm for clustering graphs with dominating diametral path, Inform. Process. Lett. 61 (1997) 121-127.
9. M. Farber, Characterization of strongly chordal graphs, Discrete Math. 43 (1983) 173-189.
10. M. Farber, Domination, independent domination, and duality in strongly chordal graphs. Discrete Appl. Math. 7 (1984) 115-130.
11. A. Farley, S. Hedetniemi, A. Proskurowski, Partitioning trees: Matching, domination, and maximum diameter, Int. J. Comput. Inform. Sci. 10(1) (1981) 55-61.
12. M.R. Garey, D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W.H. Freeman and Company, San Francisco, CA, 1979.
13. A. Gibbons, W. Rytter, Efficient Parallel Algorithms, Cambridge University Press, Cambridge, 1988.
14. F. Glover, Maximum matching in a convex bipartite graph, Naval Res. Logist. Quart. 14 (1967) 313-316.
15. M.C. Golumbic, Algorithmic graph theory and perfect graphs, Academic Press, New York, 1980.
16. M. Grötschel, L. Lovász, A. Schrijver, Polynomial algorithms for perfect graphs, Ann. Discrete Math. 21 (1984) 325-356.
17. U.I. Gupta, D.T. Lee, J.Y.-T. Leung, Efficient algorithms for interval graphs and circular-arc graphs. Networks 12 (1982) 459-467.
18. P.N. Klein, Efficient parallel algorithms for chordal graphs, Proc. 29th Annual IEEE Symp. Foundations of Computer Science, 1988, pp. 150-161.
19. N. Linial, M. Saks, Low diameter graph decomposition, Combinatorica 13 (1993) 441-454.
20. A. Moitra, R. Johnson, Parallel algorithms for maximum matching and other problems on interval graphs. Technical Report TR 927-88, Cornell University, 1988.
21. S. Olariu, J.L. Schwing, J. Zhang, Optimal parallel algorithms for problems modeled by a family of intervals, IEEE Trans. Parallel Distributed Systems 3(3) (1992) 364-374.
22. Y. Perl, M. Snir, Circuit partitioning with size and connection constraints. Networks 13 (1983) 365-375.
23. S. Poljak, A note on stable sets and colorings of graphs, Comment. Math. Univ. Carolinae 15 (1974) 307-309.
24. J. Spinrad, A. Brandstädt, L. Stewart, Bipartite permutation graphs. Discrete Appl. Math. 18 (1987) 279-292.
25. D.B. West, Introduction to Graph Theory, Prentice-Hall, Englewood Cliffs, NJ, 1996.
26. Z. Wu, R. Leahy, An optimal graph theoretic approach to data clustering: Theory and its application to image segmentation, IEEE Trans. Pattern Anal. Machine Intell. 15(11) (1993) 1101-1113.