Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences

COLLEGE OF ENGINEERING

UC Berkeley

An O(log n) Time Common CRCW PRAM Algorithm for Minimum Spanning Tree

Ramesh Subramonian

EECS Department
University of California, Berkeley
Technical Report No. UCB/CSD-92-673
March 1992

http://www.eecs.berkeley.edu/Pubs/TechRpts/1992/CSD-92-673.pdf

We present a probabilistic algorithm for finding the minimum spanning tree of a graph with n vertices and m edges on a Common CRWC PRAM. It uses expected O(log n log* n) time with ( m + n) processors and expected O(log n) time with ( m + n) log n processors. This represents a significant improvement in terms of efficiency over the previous best results for solving this problem on a Common CRCW PRAM and compares favorably with the best result for the Priority CRCW PRAM, a more powerful model. The algorithm presents a novel application of recent results on recursive *-tree data structures. An important contribution of this paper is (i) a strategy to schedule the growth of components in algorithms based on repeated graph-contractions and (ii) an amortized analysis technique to account for the scheduling overhead.


BibTeX citation:

@techreport{Subramonian:CSD-92-673,
    Author = {Subramonian, Ramesh},
    Title = {An O(log n) Time Common CRCW PRAM Algorithm for Minimum Spanning Tree},
    Institution = {EECS Department, University of California, Berkeley},
    Year = {1992},
    Month = {Mar},
    URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1992/6133.html},
    Number = {UCB/CSD-92-673},
    Abstract = {We present a probabilistic algorithm for finding the minimum spanning tree of a graph with <i>n</i> vertices and <i>m</i> edges on a Common CRWC PRAM. It uses expected <i>O</i>(log <i>n</i> log* <i>n</i>) time with (<i>m</i> + <i>n</i>) processors and expected <i>O</i>(log <i>n</i>) time with (<i>m</i> + <i>n</i>) log <i>n</i> processors. This represents a significant improvement in terms of efficiency over the previous best results for solving this problem on a Common CRCW PRAM and compares favorably with the best result for the Priority CRCW PRAM, a more powerful model. The algorithm presents a novel application of recent results on recursive *-tree data structures. An important contribution of this paper is (i) a strategy to schedule the growth of components in algorithms based on repeated graph-contractions and (ii) an amortized analysis technique to account for the scheduling overhead.}
}

EndNote citation:

%0 Report
%A Subramonian, Ramesh
%T An O(log n) Time Common CRCW PRAM Algorithm for Minimum Spanning Tree
%I EECS Department, University of California, Berkeley
%D 1992
%@ UCB/CSD-92-673
%U http://www.eecs.berkeley.edu/Pubs/TechRpts/1992/6133.html
%F Subramonian:CSD-92-673