Abstract
Given an arbitrary (bridgeless) network G=(V, E), we develop a distributed algorithm which runs on the network itself to find a small cycle cover for the network, using only local knowledge and message passing. A cycle cover C of G is a set of cycles such that every edge of E is contained in at least one cycle in C. Although the minimum cycle cover problem is conjectured to be N P-complete, our algorithm guarantees a small cycle cover of O(m + n log n) size, where n and m are the number of processors V and communication links E in the network respectively. In an asynchronous bounded delay network where message length is O(log n) bits, the algorithm requires O(n log n) time and O(mn + n 2 log n) messages in the worst case.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Alon, N. and Tarsi, M.: Covering multigraphs by simple circuits. SIAM J. Alg. Disc. Meth., 6(3) (1985) 345–350
Awerbuch, B.: Optimal distributed algorithms for minimum weight spanning tree, counting, leader election and related problems. 19th ACM Symposium on Theory of Computing (1987) 230–240
Chang, E. J. H.: Echo algorithms: depth parallel operations on general graphs. IEEE Trans. on Software Eng. SE-8(4) (1982) 391–401
Gallager, R. G., Humblet, P. A., Spira, P. M.: A distributed algorithm for minimum-weight spanning tree. ACM Trans. on Prog. Lang. and Sys. 5(1) (1983) 66–77
Itai, A., Rodeh, M.: Covering a graph by circuits. Proc. ICALP Conf. (1978) 289–299
Itai, A., Lipton, R. J., Papadimitriou, C. H., Rodeh, M.: Covering graphs by simple circuits. SIAM J. Comput. 10(4) (1991) 746–750
Klein, P., Stein, C.: A parallel algorithm for approximating the minimum cycle cover. Algorithmica 9 (1993) 23–31
Tel, G.: Topics in distributed algorithms. Cambridge International Series on Parallel Computation 1 (1991).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jennings, E., Motyčková, L. (1994). Distributed algorithms for finding small cycle covers in arbitrary networks. In: Du, DZ., Zhang, XS. (eds) Algorithms and Computation. ISAAC 1994. Lecture Notes in Computer Science, vol 834. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58325-4_172
Download citation
DOI: https://doi.org/10.1007/3-540-58325-4_172
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58325-7
Online ISBN: 978-3-540-48653-4
eBook Packages: Springer Book Archive