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
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.
|[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).|