O(n log log n)-work parallel algorithms for straight-line grid embeddings of planar graphs

Martin Fuerer*, Xin He, Ming Yang Kao, Balaji Raghavachari

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations

Abstract

A straight-line grid embedding of a planar graph is a drawing of the graph on a plane where the vertices are located at grid points and the edges are represented by nonintersecting segments of straight lines joining their incident vertices. Given an n-vertex planar graph with n ≥ 3, a straight-line embedding on a grid of size (n - 2) × (n - 2) can be computed deterministically in O(log n log log n) time with O(n log log n) work on a parallel random access machine. If randomization is used, the complexity is improved to O(log n) expected time with the same work bound. The parallel random access machine used by these algorithms allows concurrent reads and concurrent writes of the shared memory; in case of a write conflict, an arbitrary processor succeeds.

Original languageEnglish (US)
Title of host publication4th Annual ACM Symposium on Parallel Algorithms and Architectures
PublisherPubl by ACM
Pages410-419
Number of pages10
ISBN (Print)089791483X
StatePublished - Dec 1 1992
Event4th Annual ACM Symposium on Parallel Algorithms and Architectures - SPAA '92 - San Diego, CA, USA
Duration: Jun 29 1992Jul 1 1992

Other

Other4th Annual ACM Symposium on Parallel Algorithms and Architectures - SPAA '92
CitySan Diego, CA, USA
Period6/29/927/1/92

ASJC Scopus subject areas

  • Engineering(all)

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