Optimal parallel algorithms for finding cut vertices and bridges of interval graphs

We present O(log n) time algorithm 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, form an O(log n) time algorithm using n processors, which is shown to be optimal. The algorithms rely heavily on the parallel prefix algorithm.