## Parallel Tree Contraction Part 2: Further Applications (1991)

Venue: | SIAM JOURNAL ON COMPUTING |

Citations: | 29 - 3 self |

### BibTeX

@ARTICLE{Miller91paralleltree,

author = {Gary L. Miller and John H. Reif},

title = { Parallel Tree Contraction Part 2: Further Applications},

journal = {SIAM JOURNAL ON COMPUTING},

year = {1991},

volume = {20},

number = {6},

pages = {1128--1147}

}

### OpenURL

### Abstract

This paper applies the parallel tree contraction techniques developed in Miller and paper [Randomness and Computation, 5, S. Micali, ed., JAI Press, 1989, pp. 47-72] to a number of fundamental graph problems. The paper presents an time and processor, a 0-sided randomized algorithm for testing the isomorphism of trees, and an n) time, n-processor algorithm for maximal isomorphism and for common subexpression elimination. An time, n-processor algorithm for computing the canonical forms of trees and subtrees is given. An Ologn time algorithm for computing the tree of 3-connected components of a graph, an n)time algorithm for computing an explicit planar embedding of a planar graph, and an n)time algorithm for computing a canonical form for a planar graph are also given. All these latter algorithms use only processors on a Parallel Random Access Machine (PRAM) model with concurrent writes and concurrent reads.