Abstract
We present an optimal parallel algorithm for computing a cycle separator of ann-vertex embedded planar undirected graph inO(logn) time onn/logn processors. As a consequence, we also obtain an improved parallel algorithm for constructing a depth-first search tree rooted at any given vertex in a connected planar undirected graph in O(log2 n) time on n/logn processors. The best previous algorithms for computing depth-first search trees and cycle separators achieved the same time complexities, but withn processors. Our algorithms run on a parallel random access machine that permits concurrent reads and concurrent writes in its shared memory and allows an arbitrary processor to succeed in case of a write conflict.
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Communicated by D. T. Lee.
A preliminary version of this paper appeared as “Improved Parallel Depth-First Search in Undirected Planar Graphs” in theProceedings of the Third Workshop on Algorithms and Data Structures, 1993, pp. 407–420.
Supported in part by NSF Grant CCR-9101385.
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Kao, MY., Teng, SH. & Toyama, K. An optimal parallel algorithm for planar cycle separators. Algorithmica 14, 398–408 (1995). https://doi.org/10.1007/BF01192047
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DOI: https://doi.org/10.1007/BF01192047