Disjoint paths have applications in establishing bottleneck-free communication between processors in a network. The problem of finding minimum delay disjoint paths in a network directly reduces to the problem of finding the minimal disjoint paths in the graph which models the network. Previous results for this problem on chordal graphs were an O(|V| |E|²) algorithm for 2 edge disjoint paths and an O(|V| |E|) algorithm for 2 vertex disjoint paths. In this paper, we give an O(|V| |E|) algorithm for 2 vertex disjoint paths and an O(|V|+|E|) algorithm for 2 edge disjoint paths, which is a significant improvement over the previous result.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1012,
author = {C.P. Gopalakrishnan and C.R. Satyan and C. Pandu Rangan},
title = {Efficient algorithms for minimal disjoint path problems on chordal graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {15},
year = {1995},
pages = {119-145},
zbl = {0845.05084},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1012}
}
C.P. Gopalakrishnan; C.R. Satyan; C. Pandu Rangan. Efficient algorithms for minimal disjoint path problems on chordal graphs. Discussiones Mathematicae Graph Theory, Tome 15 (1995) pp. 119-145. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1012/
[000] [G 80] M.C. Golumbic, Algorithmic Graph Theory and Perfect Graphs (Academic Press, 1980).
[001] [K 75] R.M. Karp, On the computational complexity of combinatorial problems, Networks 5 (1975) 45-68. | Zbl 0324.05003
[002] [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.
[003] [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. | Zbl 0365.68026
[004] [RS 86] N. Robertson, P.D. Seymour, Graph minors XIII. The disjoint paths problem, Manuscript 1986.
[005] [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. | Zbl 0475.68042
[006] [S 89] A. Schwill, Shortest edge-disjoint paths in graphs, in: Proc. of the 6th STACS (1989) 505-516.
[007] [S 90] A. Schwill, Nonblocking graphs: Greedy algorithms to compute disjoint paths, in: Proc. of the 7th STACS (1990) 250-262.
[008] [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.