Abstract
We describe a new technique for contracting planar graphs which generalizes the tree contraction technique introduced by Miller and Reif. Our algorithm contracts a given planar graph in O(log n) rounds to one with a constant number of vertices. We use this technique to give an efficient NC solution to the following problem. It is known that a planar graph with n≥ 3 vertices has a straight-line embedding on an n−2 by n−2 grid. We show that such an embedding is computable in O(log2 n log* n) time using O(n) processors on a CREW PRAM.
This work was supported in part by the NSF under grant CCR-8805978.
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© 1991 Springer-Verlag Berlin Heidelberg
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Fürer, M., Raghavachari, B. (1991). Contracting planar graphs efficiently in parallel. In: Biswas, S., Nori, K.V. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1991. Lecture Notes in Computer Science, vol 560. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54967-6_78
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DOI: https://doi.org/10.1007/3-540-54967-6_78
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