Abstract
In this paper, sequential and parallel algorithms are presented to find a maximum independent set with largest weight in a weighted permutation graph. The sequential algorithm, which is designed based on dynamic programming, runs in timeO(nlogn) and requiresO(n) space. The parallel algorithm runs inO(log2 n) time usingO(n 3/logn) processors on the CREW PRAM, orO(logn) time usingO(n 3) processors on the CRCW PRAM.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. Atallah, R. Cole, and M. Goodrich,Cascading divide-and-conquer: a technique for designing parallel algorithms, Proceedings of the 28th Annual Symposium on Foundations of Computer Science, 1987, pp. 151–120.
M. J. Atallah, G. K. Manacher, and J. Urrutia,Finding a minimum independent dominating set in a permutation graph, Discrete Applied Mathematics, vol. 21, pp. 177–183, 1988.
A. Brandstadt and D. Kratsch,On domination problems for permutation and other graphs, Theoretical Computer Science, vol. 54, pp. 181–198, 1987.
L. Chen,Logarithmic time NC algorithms for comparability graphs and circle graphs, Lecture Notes in Computer Science: Advances in Computing and Information, vol. 497, pp. 383–394, 1991.
M. Farber and J. M. Keil,Domination in permutation graphs, Journal of Algorithms, vol. 6, pp. 309–321, 1985.
M. R. Garey and D. S. Johnson,Computers and Intractability: a Guide to the Theory of NP-Completeness, Freeman, San Francisco, CA, 1979.
M. C. Golumbic,Algorithmic Graph Theory and Perfect Graphs, Academic Press, N.Y., 1980.
D. Helmbold and E. Mayr,Perfect and parallel algorithms, Proceedings of the International Conference on Parallel Processing, 1986, pp. 853–860.
R. G. Karlsson and M. H. Overmars,Scanline algorithms on a grid, BIT, vol. 28, pp. 227–241, 1988.
D. E. Knuth,The Art of Computer Programming, vol. 1, Addison-Wesley, Reading, MA., 1968.
D. Kozen, U. V. Vazirani, and V. V. Vazirani,NC algorithms for comparability graphs, interval graphs, and testing for unique perfect matching, Proceedings of the Fifth Conference on Foundation of Software Technology and Theoretical Computer Science, New Dehli, 1985, pp. 498–503.
C. L. Liu,Introduction to Combinatorial Mathematics, McGraw-Hill, 1968.
A. Pnueli, A. Lempel, and S. Even,Transitive orientation of graphs and identification of permutation graphs, Can. J. Math., vol. 23, pp. 160–175, 1971.
B. Schieber and U. Vishkin,On finding lowest common ancestors: simplification and parallelization, SIAM Journals on Computing, vol. 17, pp. 1253–1262, 1988.
J. Spinrad,On comparability and permutation graphs, SIAM Journals on Computing, vol. 14, pp. 658–670, 1985.
J. Spinrad, A. Brandstadt, and L. Stewart,Bipartite permutation graphs, Discrete Applied Mathematics, vol. 18, pp. 279–292, 1987.
K. J. Supowit,Decomposing a set of points into chains, with applications to permutation and circle graphs, Information Processing Letters, vol. 21, pp. 249–252, 1985.
K. H. Tsai and W. L. Hsu,Fast algorithms for the dominating set problem on permutation graphs, Lecture Notes in Computer Science: Algorithms, vol. 450, pp. 109–117, 1990.
Y. Zhang,Parallel algorithms for problems involving directed graphs, Ph.D. Thesis, Drexel University, 1986.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Yu, CW., Chen, GH. The weighted maximum independent set problem in permutation graphs. BIT 32, 609–618 (1992). https://doi.org/10.1007/BF01994845
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01994845