# Finding triconnected components by local replacements

## Abstract

We present an almost-optimal parallel algorithm for finding triconnected components on a CRCW PRAM. The time complexity of our algorithm is O(*log* n) and the processor-time product is O((m + n)·α(m, n)) where α is the inverse Ackerman function; here n is the number of vertices, and m is the number of edges in the graph. The algorithm is optimal for m≥n *log** n. Our algorithm, like other parallel algorithms for this problem, is based on ear decomposition but it employs a new technique, local replacement, to improve the complexity. Only the need to find connected components, for which no optimal parallel algorithm that runs in O(*log* n) time is known, prevents our algorithm from achieving optimality on an EREW PRAM.

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