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Processor efficient parallel algorithms for the two disjoint paths problem, and for finding a Kuratowski homeomorph

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3 Author(s)
Khuller, S. ; Dept. of Comput. Sci., Cornell Univ., Ithaca, NY, USA ; Mitchell, S.G. ; Vazirani, Vijay V.

Given a graph G and two pairs of vertices s1, t1 and s2, t2, the two disjoint paths problem asks for vertex-disjoint paths connecting si with ti, i=1, 2. A fast parallel (NC) algorithm is given for this problem, which has applications in certain routing situations. If G is nonplanar, an algorithm that finds a Kuratowski homeomorph in G (i.e. a subgraph homeomorphic to K3.3 or K5) is given. This complements the known NC planarity algorithms, which give a planar embedding in the positive case; the algorithm provides a certificate of nonplanarity in the negative case. Both algorithms are processor efficient; in each case, the processor-time product is within a polylogarithmic factor of the best known sequential algorithm

Published in:

Foundations of Computer Science, 1989., 30th Annual Symposium on

Date of Conference:

30 Oct-1 Nov 1989

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