Optimal Parallel Construction of Prescribed Tournaments

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
```