## Abstract

Part I of this paper presented a novel technique for approximate parallel scheduling and a new logarithmic time optimal parallel algorithm for the list ranking problem. In this part, we give a new logarithmic time parallel (PRAM) algorithm for computing the connected components of undirected graphs which uses this scheduling technique. The connectivity algorithm is optimal unless m = o(n log^{*} n) in graphs of n vertices and m edges. (log^{(k)} denotes the kth iterate of the log function and log^{*} n denotes the least i such that log^{(i)} n ≤ 2). Using known results, this new algorithm implies logarithmic time optimal parallel algorithms for a number of other graph problems, including biconnectivity, Euler tours, strong orientation and st-numbering. Another contribution of the present paper is a parallel union/find algorithm.

Original language | English (US) |
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Pages (from-to) | 1-47 |

Number of pages | 47 |

Journal | Information and Computation |

Volume | 92 |

Issue number | 1 |

DOIs | |

State | Published - May 1991 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Information Systems
- Computer Science Applications
- Computational Theory and Mathematics