# Parallel algorithms for series parallel graphs

## Abstract

In this paper, a parallel algorithm is given that, given a graph *G*=(*V, E*), decides whether *G* is a series parallel graph, and if so, builds a decomposition tree for *G* of series and parallel composition rules. The algorithm uses *O*(log¦*E*¦log^{*}¦*E*¦) time and *O*(¦*E*¦) operations on an EREW PRAM, and*O*(log¦*E*¦) time and *O*(¦*E*¦) operations on a CRCW PRAM (note that if *G* is a simple series parallel graph, then ¦*E*¦=*O*(¦*V*¦)). With the same time and processor resources, a tree-decomposition of width at most two can be built of a given series parallel graph, and hence, very efficient parallel algorithms can be found for a large number of graph problems on series parallel graphs, including many well known problems, e.g., all problems that can be stated in monadic second order logic. The results hold for undirected series parallel graphs graphs, as well as for directed series parallel graphs.

## Keywords

Decomposition Tree Simple Path Reduction Rule Parallel Edge Conflict Graph## Preview

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