A nearly optimal parallel algorithm for constructing maximal independent set in planar graphs

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Abstract

This paper presents an efficient parallel algorithm for constructing maximal independent set in planar graphs. The algorithm runs in O(log2n) time with O(n) processors on a PRAM and is within an O(log2n) factor of optimal. The best previously known algorithm for this problem takes O(log2n) time with O(n3) processors. The key subroutine of the algorithm is an O(logn) time, O(n) processor parallel algorithm for constructing a maximal independent set in a one-page planar graph. This subroutine may be of independent interest.

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This work was supported in part by an Ohio State University Presidential Fellowship.

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Present affiliation: Department of Computer Science, State University of New York at Buffalo, Buffalo, NY 14260, U.S.A.