Advertisement

A Linear-Time Algorithm to Find Four Independent Spanning Trees in Four-Connected Planar Graphs

  • Kazuyuki Miura
  • Daishiro Takahashi
  • Shin-ichi Nakano
  • Takao Nishizeki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1517)

Abstract

Given a graph G, a designated vertex r and a natural number k, we wish to find k independent spanning trees of G rooted at r, that is, k spanning trees such that, for any vertex v, the k paths connecting r and v in the k trees are internally disjoint in G. In this paper we give a linear-time algorithm to find four independent spanning trees in a 4-connected planar graph rooted at any vertex.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bao, F., Igarashi, Y.: Reliable broadcasting in product networks with By-zantime faults. In: Proc. 26th Annual International Symposium on Fault-Tolelant Computing (FTCS 1996), pp. 262–271 (1996)Google Scholar
  2. Di Battista, G., Tamassia, R., Vismara, L.: Output-sensitive reporting of disjoint paths. Technical Report CS-96-25, Department of Computer Science, Brown University (1996)Google Scholar
  3. Chrobak, M., Kant, G.: Convex grid drawings of 3-connected planar graphs. Technical Report RUU-CS-93-45, Department of Computer Science, Utrecht University (1993)Google Scholar
  4. Cheriyan, J., Maheshwari, S.N.: Finding nonseparating induced cycles and independent spanning trees in 3-connected graphs. J. Algorithms 9, 507–537 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  5. Dolev, D., Halpern, J.Y., Simons, B., Strong, R.: A new look at fault tolerant network routing. In: Proc. 16th Annual ACM Symposium on Theory of Computing, pp. 526–535 (1984)Google Scholar
  6. Even, S.: Graph Algorithms. Computer Science Press, Potomac (1979)zbMATHGoogle Scholar
  7. Huck, A.: Independent trees in Graphs. Graphs and Combinatorics 10, 29–45 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  8. Itai, A., Rodeh, M.: The multi-tree approach to reliability in distributed networks. Information and Computation 79, 43–59 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  9. Kant, G., He, X.: Two algorithms for finding rectangular duals of planar graphs. In: van Leeuwen, J. (ed.) WG 1993. LNCS, vol. 790, pp. 396–410. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  10. Khuller, S., Schieber, B.: On independent spanning trees. Information Processing Letters 42, 321–323 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  11. Nakano, S., Rahman, M.S., Nishizeki, T.: A linear time algorithm for four-partitioning four-connected planar graphs. Information Processing Letters 62, 315–322 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  12. Obokata, K., Iwasaki, Y., Bao, F., Igarashi, Y.: Independent spanning trees of product graphs and their construction. In: D’Amore, F., Marchetti-Spaccamela, A., Franciosa, P.G. (eds.) WG 1996. LNCS, vol. 1197, pp. 338–351. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  13. Zehavi, A., Itai, A.: Three tree-paths. J. Graph Theory 13, 175–188 (1989)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Kazuyuki Miura
    • 1
  • Daishiro Takahashi
    • 1
  • Shin-ichi Nakano
    • 1
  • Takao Nishizeki
    • 1
  1. 1.Graduate School of Information SciencesTohoku UniversitySendaiJapan

Personalised recommendations