### 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 - 1991 |

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### ASJC Scopus subject areas

- Computational Theory and Mathematics

### Cite this

**Approximate parallel scheduling. II. Applications to logarithmic-time optimal parallel graph algorithms.** / Cole, Richard; Vishkin, Uzi.

Research output: Contribution to journal › Article

*Information and Computation*, vol. 92, no. 1, pp. 1-47. https://doi.org/10.1016/0890-5401(91)90019-X

}

TY - JOUR

T1 - Approximate parallel scheduling. II. Applications to logarithmic-time optimal parallel graph algorithms

AU - Cole, Richard

AU - Vishkin, Uzi

PY - 1991

Y1 - 1991

N2 - 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.

AB - 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.

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UR - http://www.scopus.com/inward/citedby.url?scp=0026155384&partnerID=8YFLogxK

U2 - 10.1016/0890-5401(91)90019-X

DO - 10.1016/0890-5401(91)90019-X

M3 - Article

AN - SCOPUS:0026155384

VL - 92

SP - 1

EP - 47

JO - Information and Computation

JF - Information and Computation

SN - 0890-5401

IS - 1

ER -