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Optimal parallel algorithms for finding cut vertices and bridges of interval graphs. (English) Zbl 0764.68054
Summary: We present \(O(\log n)\) time algorithms in the EREW PRAM model, using \(n/\log n\) processors, to find cut vertices, bridges, and blocks (often called biconnected components) of an interval graph having \(n\) vertices. It is assumed the interval graph is represented by an interval model, with ends presorted. If the ends are not presorted, our algorithms, preceded by an optimal sort, from an \(O(\log n)\) time algorithm using \(n\) processors, which is shown to be optimal. The algorithms rely heavily on the parallel prefix algorithm.

MSC:
68W15 Distributed algorithms
68Q25 Analysis of algorithms and problem complexity
68R10 Graph theory (including graph drawing) in computer science
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