# 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