# Efficient parallel algorithms on interval graphs

## Abstract

We design efficient parallel algorithms for solving several problems on interval graphs. The problems include finding a BFS-tree and DFS-tree, articulation points and bridges, and minimum coloring. Each of our algorithms requires *O*(log *n*) time employing *O*(*n*) processors on the EREW PRAM model, where *n* is the number of vertices. The proposed algorithms for computing articulation points and bridges have better performance in terms of the cost (i.e, processor-time product) than the existing algorithms in [RR90], yet having the same time complexity. Our novel approach to the construction of BFS tree is based on elegantly capturing the structure of a given collection of intervals. This structure reveals important properties of the corresponding interval graph, and is found to be instrumental in solving many other problems on such graphs. Although the time- and processor-complexities of the proposed DFS-tree construction or minimum-coloring is comparable with the best-known ones [KI89], our approach to these problems are new. For example, the approach to the construction of a DFS tree is based on reducing the problem into an *all dominating neighbors* (ADN) problem; while that to the minimum coloring is by transforming this problem into a linked list ranking problem.

## Keywords

Parallel Algorithm Interval Graph Articulation Point Nest Level Back Edge## Preview

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