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Processor Efficient Parallel Algorithms for the Two Disjoint Paths Problem, and for Finding a Kuratowski Homeomorph

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We give an NC algorithm for finding vertex disjoint s1,t1 and s2,t2 paths in an undirected graph G. An important step in solving the general problem is solving the planar case. A new structural property yields the parallelization, as well as a simpler linear time sequential algorithm for this case. We extend the algorithm to the non-planar case by giving an NC algorithm for finding a Kuratowski homeomorph, and, in particular, a homeomorph of K3,3, in a non-planar graph. Our algorithms are processor efficient; in each case, the processor-time product of our algorithms is within a polylogarithmic factor of the best known sequential algorithm.

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1989-04

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Cornell University

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computer science; technical report

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http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR89-960

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technical report

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