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ArticleOriginal scientific text

Title

Edge-disjoint paths in permutation graphs

Authors 1, 1

Affiliations

  1. Department of Computer Science, Indian Institute of Technology

Abstract

In this paper we consider the following problem. Given an undirected graph G = (V,E) and vertices s₁,t₁;s₂,t₂, the problem is to determine whether or not G admits two edge-disjoint paths P₁ and P₂ connecting s₁ with t₁ and s₂ with t₂, respectively. We give a linear (O(|V|+|E|)) algorithm to solve this problem on a permutation graph.

Keywords

ENG
algorithm, bridge, connectivity, disjoint paths, permutation graph

Bibliography

  1. [AKP] K. Arvind, V. Kamakoti, C. Pandu Rangan, Efficient Parallel Algorithms for Permutation Graphs, to appear in Journal of Parallel and Distributed Computing.
  2. [BM 80] J. A. Bondy, U.S.R. Murty, Graph Theory with Applications, (Macmillan Press, 1976).
  3. [C 80] A. Cypher, An approach to the k paths problem, Proc. of the 12th STOC (1980) 211-217.
  4. [G 80] M. C. Golumbic, Algorithmic Graph Theory and Perfect Graphs, (Academic Press, 1980).
  5. [F 85] A. Frank, Edge-disjoint paths in planar graphs, J. Combin. Theory (B) 39 (1985) 164-178, doi: 10.1016/0095-8956(85)90046-2.
  6. [GP] C. P. Gopalakrishnan, C. Pandu Rangan, The two paths problem on permutation graphs, (submitted).
  7. [LR 78] A. LaPaugh, R. L. Rievest, The subgraph homeomorphism problem, Proc. of the 10th STOC (1978) 40-50.
  8. [O 80] T. Ohtsuki, The two disjoint path problem and wire routing design, in: Proc. of the 17th Symp. of Res. Inst. of Electrical Comm. (1980) 257-267.
  9. [PS 78] Y. Perl, Y. Shiloach, Finding two disjoint paths between two pairs of vertices in graph, J. of the ACM 25 (1978) 1-9, doi: 10.1145/322047.322048.
  10. [RP] P. B. Ramprasad, C. Pandu Rangan, A new linear time algorithm for the two path problem on planar graphs, to appear.
  11. [S 90] A. Schwill, Nonblocking graphs: Greedy algorithms to compute disjoint paths, Proc. of the 7th STACS (1990) 250-262.
  12. [S 80] Y. Shiloach, A polynomial solution to the undirected two paths problem, J. of the ACM 27 (1980) 445-456, doi: 10.1145/322203.322207.
  13. [S 83] J. Spinrad, Transitive orientation in O(n²) time, Proc. of Fifteenth ACM Symposium on the Theory of Computing (1983) 457-466, doi: 10.1145/800061.808777.
  14. [SP 91] A. Srinivasa Rao, C. Pandu Rangan, Linear algorithms for parity path and two path problems on circular arc graphs, BIT 31 (1991) 182-193.
  15. [KPS 91] S. V. Krishnan, C. Pandu Rangan, S. Seshadri, A. Schwill, Two Disjoint Paths in Chordal graphs, Technical report, 2/91, February 1991, University of Oldenburg, Germany.
Discussiones Mathematicae Graph Theory
1995/15/1
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Pages:
59-72
Main language of publication
English
Received
1994-05-04
Published
1995
Exact and natural sciences