Abstract
Switch graphs as introduced in [Coo03] are a natural generalization of graphs where edges are interpreted as train tracks connecting switches: Each switch has an obligatory incident edge which has to be used by every path going through this switch. We prove that the simple reachability problem in switch graphs is NP-complete in general, but we describe a polynomial time algorithm for the undirected case. As an application, this can be used to find an augmenting path for bigamist matchings and thus iteratively construct a maximum bigamist matching for a given bipartite graph with red and blue edges, that is the maximum set of vertex disjoint triples consisting of one bigamist vertex connected to two monogamist vertices with two different colors. This this gives an independent direct solution to an open problem in [SGYB05].
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Allender, E., Reinhardt, K., Zhou, S.: Isolation matching and counting uniform amd nonuniform upper bounds. Journal of Computer and System Sciences 59, 164–181 (1999)
Cook, M.: Still life theory. In: Moore, C., Griffeath, D. (eds.) New Constructions in Cellular Automata, vol. 226, pp. 93–118. Oxford University Press, US (2003) (Santa Fe Institute Studies on the Sciences of Complexity)
Cornuejols, G.: General factors of graphs. Journal for Combinatorial Theory B 45, 185–198 (1988)
Edmonds, J.: Paths, trees, and flowers. Canad. J. Math. 17, 449–467 (1965)
Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-completeness. Freeman, San Francisco (1978)
Hopcroft, J.E., Karp, R.M.: An n\(^{\mbox{\small 5/2}}\) algorithm for maximum matchings in bipartite graphs. SIAM J. Comput. 2(4), 225–231 (1973)
Jones, N.D.: Space bounded reducibility among combinatorial problems. Journal of Computer and System Sciences 11, 68–85 (1975)
Kirkpatrik, D.G., Hell, P.: On the complexity of general graph factor problems. SIAM J. Comput. 12(3), 601–608 (1983)
Lovasz, L.: The factorization of graphs, II. Acta Math. Acad. Sci. Hungar. 23, 223–246 (1972)
Reingold, O.: Undirected st-connectivity in log-space. In: STOC 2005: Proceedings of the thirty-seventh annual ACM symposium on Theory of computing, pp. 376–385. ACM, New York (2005)
Sharan, R., Gramm, J., Yakhini, Z., Ben-Dor, A.: Multiplexing schemes for generic SNP genotyping assays. Journal of Computational Biology 12, 514–533 (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Reinhardt, K. (2009). The Simple Reachability Problem in Switch Graphs. In: Nielsen, M., Kučera, A., Miltersen, P.B., Palamidessi, C., Tůma, P., Valencia, F. (eds) SOFSEM 2009: Theory and Practice of Computer Science. SOFSEM 2009. Lecture Notes in Computer Science, vol 5404. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-95891-8_42
Download citation
DOI: https://doi.org/10.1007/978-3-540-95891-8_42
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-95890-1
Online ISBN: 978-3-540-95891-8
eBook Packages: Computer ScienceComputer Science (R0)