The Simple Reachability Problem in Switch Graphs

  • Klaus Reinhardt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5404)


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].


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [ARZ99]
    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)MathSciNetCrossRefMATHGoogle Scholar
  2. [Coo03]
    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)Google Scholar
  3. [Cor88]
    Cornuejols, G.: General factors of graphs. Journal for Combinatorial Theory B 45, 185–198 (1988)MathSciNetCrossRefMATHGoogle Scholar
  4. [Edm65]
    Edmonds, J.: Paths, trees, and flowers. Canad. J. Math. 17, 449–467 (1965)MathSciNetCrossRefMATHGoogle Scholar
  5. [GJ78]
    Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-completeness. Freeman, San Francisco (1978)MATHGoogle Scholar
  6. [HK73]
    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)MathSciNetCrossRefMATHGoogle Scholar
  7. [Jon75]
    Jones, N.D.: Space bounded reducibility among combinatorial problems. Journal of Computer and System Sciences 11, 68–85 (1975)MathSciNetCrossRefMATHGoogle Scholar
  8. [KH83]
    Kirkpatrik, D.G., Hell, P.: On the complexity of general graph factor problems. SIAM J. Comput. 12(3), 601–608 (1983)MathSciNetCrossRefMATHGoogle Scholar
  9. [Lov72]
    Lovasz, L.: The factorization of graphs, II. Acta Math. Acad. Sci. Hungar. 23, 223–246 (1972)MathSciNetCrossRefMATHGoogle Scholar
  10. [Rei05]
    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)CrossRefGoogle Scholar
  11. [SGYB05]
    Sharan, R., Gramm, J., Yakhini, Z., Ben-Dor, A.: Multiplexing schemes for generic SNP genotyping assays. Journal of Computational Biology 12, 514–533 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Klaus Reinhardt
    • 1
  1. 1.Universität TübingenSand 13Germany

Personalised recommendations