Elsevier

Journal of Algorithms

Volume 12, Issue 3, September 1991, Pages 409-430
Journal of Algorithms

Efficient parallel algorithms for series parallel graphs

https://doi.org/10.1016/0196-6774(91)90012-NGet rights and content

Abstract

We present efficient parallel algorithms for solving three problems for series parallel graphs: 3-coloring, depth-first spanning tree, and breadth-first spanning tree. If the input is given by the decomposition tree, the first two problems can be solved in O(log n) time with O(nlog n) processors, the last problem can be solved in O(log n log log n) time with O(n) processors. We also present a parallel algorithm for recognizing series parallel graphs and constructing decomposition trees. This algorithm takes O(log2 n + log m) time with O(n + m) processors, where n (m) is the number of vertices (edges) in the graph.

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    Research supported in part by NSF grant CCR-9011214.

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