An Optimal Randomised Logarithmic Time Connectivity Algorithm for the EREW PRAM

Shay Halperin, Uri Zwick
<span title="">1996</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="" style="color: black;">Journal of computer and system sciences (Print)</a> </i> &nbsp;
Improving a long chain of works we obtain a randomised EREW PRAM algorithm for nding the connected components of a graph G = (V; E) with n vertices and m edges in O(logn) time using an optimal number of O((m + n)= log n) processors. The result returned by the algorithm is always correct. The probability that the algorithm will not complete in O(log n) time is o(n ?c ) for any c > 0. Johnson and Metaxas have later shown JM92] that their algorithm can also be implemented in the EREW PRAM model.
more &raquo; ... about the same time, Karger, Nisan and Parnas KNP92] used the interesting technique of short random walks on graphs, developed initially by Aleliunas, Karp, Lipton, Lovasz and Racko AKL + 79], to develop a randomised EREW PRAM algorithm that runs in either O(log n) time using O((n 1+ +m)= log n) processors, for any > 0, or in O(log n log log n) time using
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1006/jcss.1996.0078</a> <a target="_blank" rel="external noopener" href="">fatcat:ksh55czujvabrhdxgqzjsqbrci</a> </span>
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