Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences

COLLEGE OF ENGINEERING

UC Berkeley

Optimal Parallel Construction of Prescribed Tournaments

Danny Soroker

EECS Department
University of California, Berkeley
Technical Report No. UCB/CSD-87-371
September 1987

http://www.eecs.berkeley.edu/Pubs/TechRpts/1987/CSD-87-371.pdf

A tournament is a digraph in which every pair of vertices is connected by exactly one arc. The score list of a tournament is the sorted list of the out-degrees of its vertices. Given a non-decreasing sequence of non-negative integers, is it the score list of some tournament? There is a simple test for answering this question. There is also a simple sequential algorithm for constructing a tournament with a given score list. However, this algorithm has a greedy nature, and seems hard to parallelize. We present a simple parallel algorithm for the construction problems. Our algorithm runs in time O(log n) and uses O( n^2/logn) processors on a CREW PRAM, where n is the number of vertices. Since the size of the output is Omega( n^2), our algorithm achieves optimal speedup.


BibTeX citation:

@techreport{Soroker:CSD-87-371,
    Author = {Soroker, Danny},
    Title = {Optimal Parallel Construction of Prescribed Tournaments},
    Institution = {EECS Department, University of California, Berkeley},
    Year = {1987},
    Month = {Sep},
    URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1987/6225.html},
    Number = {UCB/CSD-87-371},
    Abstract = {A tournament is a digraph in which every pair of vertices is connected by exactly one arc. The score list of a tournament is the sorted list of the out-degrees of its vertices. Given a non-decreasing sequence of non-negative integers, is it the score list of some tournament? There is a simple test for answering this question. There is also a simple sequential algorithm for constructing a tournament with a given score list. However, this algorithm has a greedy nature, and seems hard to parallelize. We present a simple parallel algorithm for the construction problems. Our algorithm runs in time <i>O</i>(log<i>n</i>) and uses <i>O</i>(<i>n</i>^2/log</i>n</i>) processors on a CREW PRAM, where <i>n</i> is the number of vertices. Since the size of the output is Omega(<i>n</i>^2), our algorithm achieves optimal speedup.}
}

EndNote citation:

%0 Report
%A Soroker, Danny
%T Optimal Parallel Construction of Prescribed Tournaments
%I EECS Department, University of California, Berkeley
%D 1987
%@ UCB/CSD-87-371
%U http://www.eecs.berkeley.edu/Pubs/TechRpts/1987/6225.html
%F Soroker:CSD-87-371