Abstract
In this paper, we study the problem of computing the minimum number of searchers who can capture an intruder hiding in a graph. We propose a linear time algorithm for computing the vertex separation and the optimal layout for a unicyclic graph. The best algorithm known so far is given by Ellis et al. (2004) and needs O(n logn) time, where n is the number of vertices in the graph. By a linear-time transformation, we can compute the search number and the optimal search strategy for a unicyclic graph in linear time. We show how to compute the search number for a k-ary cycle-disjoint graph. We also present some results on approximation algorithms.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bienstock, D., Seymour, P.: Monotonicity in graph searching. Journal of Algorithms 12, 239–245 (1991)
Ellis, J., Sudborough, I., Turner, J.: The vertex separation and search number of a graph. Information and Computation 113, 50–79 (1994)
Ellis, J., Markov, M.: Computing the vertex separation of unicyclic graphs. Information and Computation 192, 123–161 (2004)
Fellows, M., Langston, M.: On search, decision and the efficiency of polynomial time algorithm. In: 21st ACM Symp. on Theory of Computing, pp. 501–512. ACM Press, New York (1989)
Frankling, M., Galil, Z., Yung, M.: Eavesdropping games: A graph-theoretic approach to privacy in distributed systems. Journal of ACM 47, 225–243 (2000)
Kinnersley, N.: The vertex separation number of a graph equals its path-width. Information Processing Letters 42, 345–350 (1992)
Kirousis, L.M., Papadimitriou, C.H.: Searching and pebbling. Theoretical Computer Science 47, 205–218 (1986)
LaPaugh, A.S.: Recontamination does not help to search a graph. Journal of ACM 40, 224–245 (1993)
Megiddo, N., Hakimi, S.L., Garey, M., Johnson, D., Papadimitriou, C.H.: The complexity of searching a graph. Journal of ACM 35, 18–44 (1988)
Peng, S., Ho, C., Hsu, T., Ko, M., Tang, C.: Edge and node searching problems on trees. Theoretical Computer Science 240, 429–446 (2000)
Yang, B., Zhang, R., Cao, Y.: Searching cycle-disjoint graphs. Technical report CS-2006-05, Department of Computer Science, University of Regina (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yang, B., Zhang, R., Cao, Y. (2007). Searching Cycle-Disjoint Graphs. In: Dress, A., Xu, Y., Zhu, B. (eds) Combinatorial Optimization and Applications. COCOA 2007. Lecture Notes in Computer Science, vol 4616. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73556-4_6
Download citation
DOI: https://doi.org/10.1007/978-3-540-73556-4_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73555-7
Online ISBN: 978-3-540-73556-4
eBook Packages: Computer ScienceComputer Science (R0)