TY - JOUR

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

AU - Cole, Richard

AU - Vishkin, Uzi

N1 - Funding Information:
*This research was supported in part by NSF Grants DCR-84-01633, CCR-8702271, CCR-8902221 and CCR-8906949 by ONR Grant NOOO14-85-K-0046, by an IBM faculty development award, and by a John Simon Guggenheim Memorial Foundation Fellowship. + This research was supported in part by NSF Grants NSF-CCR-8615337, DCR-8413359 and CCR-8906949, ONR Grant N00014-85-K-0046, by the Applied Mathematical Science subprogram of the office of Energy Research, U.S. Department of Energy under Contract DE-AC02-76ER03077, and by the Foundation for Research in Electronics, Computers, and Communication, administered by the Israeli Academy of Sciences and Humanities.

PY - 1991/5

Y1 - 1991/5

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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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 -