DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory 15(2) (1995) 1147-166
DOI: 10.7151/dmgt.1013

A LINEAR ALGORITHM FOR THE TWO PATHS PROBLEM ON PERMUTATION GRAPHS

C.P. Gopalakrishnan and C. Pandu Rangan

Department of Computer Science
Indian Institute of Technology
Madras 600 036, India

e-mail: rangan@iitm.ernet.in

Abstract

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

Keywords: algorithm, bridge, connectivity, disjoint paths, permutation graph, two paths problem.

1991 Mathematics Subject Classification: 05C38, 05C85.

References

[BM 76] J.A. Bondy, U.S.R. Murthy, Graph Theory with Applications (Academic Press, 1976).
[ET 75] S. Even, R.E. Tarjan, Network flow and testing graph connectivity, SIAM J. Comput. 4 (1975) 507-518, doi: 10.1137/0204043.
[HT 74] J.E. Hopcroft, R.E. Tarjan, Efficient planarity testing, J. ACM 21 (1974) 549-568, doi: 10.1145/321850.321852.
[G 80] M.C. Golumbic, Algorithmic Graph Theory and Perfect Graphs (Academic Press, 1980).
[MT 89] B. Mishra, R.E. Tarjan, A linear time algorithm for finding an ambitus (Technical Report 464, August 1989, New York University).
[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.
[PS 78] Y. Perl, Y. Shiloach, Finding two disjoint paths between two pairs of vertices in a graph, J. of the ACM 25 (1978) 1-9, doi: 10.1145/322047.322048.
[RP] P.B. Ramprasad, C. Pandu Rangan, A new linear time algorithm for the two path problem on planar graphs (Technical Report, Department of Computer Science, IIT, Madras, 1991).
[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.
[S 83] J. Spinrad, Transitive orientation in  O(n2) time, In: Proc. of Fifteenth ACM Symposium on the Theory of Computing (1983) 457-466, doi: 10.1145/800061.808777.
[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).