@MISC{Eppstein92parallelrecognition, author = {David Eppstein}, title = {Parallel Recognition of Series-Parallel Graphs}, year = {1992} }

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Abstract

Recently, He and Yesha gave an algorithm for recognizing directed series parallel graphs, in time O(log 2 n) with linearly many EREW processors. We give a new algorithm for this problem, based on a structural characterization of series parallel graphs in terms of their ear decompositions. Our algorithm can recognize undirected as well as directed series parallel graphs. It can be implemented in the CRCW model of parallel computation to take time O(log n). In the EREW model the time is O(log 2 n) but the number of processors required improves the bounds of the previous algorithm. 1 Introduction A directed graph G is two-terminal series parallel, with terminals s and t, if it can be produced by a sequence of the following operations: 1. Create a new graph, consisting of a single edge directed from s to t. 2. Given two two-terminal series parallel graphs X and Y , with terminals s X , t X , s Y , and t Y , form a new graph G = P (X,Y ) by identifying s = s X = s Y and t = ...