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A fast algorithm for maximum integral two-commodity flow in planar graphs

Published: 16 November 1993 Publication History

Abstract

We consider in this note the maximum integral two-commodity flow problem in augmented planar graphs, that is with both source sink edges added. We provide an O(nlogn) simple algorithm for finding a maximum integral two-commodity flow in augmented planar graphs.

References

[1]
F. Barahoma, Planar multicommodity flow, max cut, and the Chinese post-man problem, Tech. Rept. 87454-OR (1987).
[2]
J.A. Bondy, U.S.R. Murty, Graph Theory with Applications, Elsevier, New York, 1976.
[3]
K.S. Booth, G.S. Lueker, Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms, J. Comput. System Sci., 13 (1976) 335-379.
[4]
S.V. Even, A. Itai, A. Shamir, On the complexity of the timetable and multicommodity flow problem, SIAM J. Comput., 5 (1976) 88-124.
[5]
A. Frank, Packing paths, circuits and cuts¿a survey, Tech. Rept. 88532-OR (1988).
[6]
G.N. Frederickson, Fast algorithms for shortest paths in planar graphs, with applications, SIAM J. Comput., 16 (1987) 1004-1022.
[7]
T.C. Hu, Multi-commodity network flows, Oper. Res., 11 (1963) 334-360.
[8]
E. Korach, Packing of T-cuts, and other aspects of dual integrality, in: Ph.D. thesis, University of Waterloo, Waterloo, Ont, 1982.
[9]
E. Korach, M. Penn, Tight integral duality gap in the Chinese postman problem, in: Tech. Rept. 360, Department of Computer Science, Technion, Haifa, 1985.
[10]
M.V. Lomonosov, On the planar integer two-flow problem, Combinatorica, 3 (1983) 207-218.
[11]
Mei Gu Guan, Graphic programming using odd or even points, Chinese Math., 1 (1962) 273-277.
[12]
M. Middendorf, F. Pfeiffer, On the complexity of the disjoint path problem, Tech. Rept. 89585-OR (1989).
[13]
A. Sebo, Integer plane multicommodity flows with a bounded number of demands, Tech. Rept. 885340-OR (1988).
[14]
P.D. Seymour, On odd cuts and plane multicommodity flow, Proc. London Math. Soc., 42 (1981) 178-192.

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    Published In

    cover image Discrete Applied Mathematics
    Discrete Applied Mathematics  Volume 47, Issue 1
    Nov. 16, 1993
    83 pages
    ISSN:0166-218X
    Issue’s Table of Contents

    Publisher

    Elsevier Science Publishers B. V.

    Netherlands

    Publication History

    Published: 16 November 1993

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