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Edge-disjoint routing in plane switch graphs in linear time

Published: 01 July 2004 Publication History

Abstract

By a switch graph, we mean an undirected graph G = (PW, E) such that all vertices in P (the plugs) have degree one and all vertices in W (the switches) have even degrees. We call G plane if G is planar and can be embedded such that all plugs are in the outer face. Given a set (s1, t1), …,(sk, tk) of pairs of plugs, the problem is to find edge-disjoint paths p1, …, pk such that every pi connects si with ti. The best asymptotic worst-case complexity known so far is quadratic in the number of vertices. In this article, a linear, and thus asymptotically optimal, algorithm is introduced. This result may be viewed as a concluding "keystone" for a number of previous results on various special cases of the problem.

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Published In

cover image Journal of the ACM
Journal of the ACM  Volume 51, Issue 4
July 2004
181 pages
ISSN:0004-5411
EISSN:1557-735X
DOI:10.1145/1008731
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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 July 2004
Published in JACM Volume 51, Issue 4

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  1. Planar graphs
  2. edge-disjoint paths

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  • (2012)SWITCHING GRAPHSInternational Journal of Foundations of Computer Science10.1142/S012905410900693020:05(869-886)Online publication date: 30-Apr-2012
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  • (2008)Switching GraphsElectronic Notes in Theoretical Computer Science (ENTCS)10.1016/j.entcs.2008.12.035223(119-135)Online publication date: 1-Dec-2008
  • (2008)The weighted link ring loading problemJournal of Combinatorial Optimization10.1007/s10878-007-9136-718:1(38-50)Online publication date: 5-Jan-2008

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