Constructing Random Steiner Triple Systems: An Experimental Study

TL;DR

This paper evaluates existing algorithms for generating random Steiner triple systems, compares their properties with theoretical expectations, and proposes modifications to improve their performance for different system sizes.

Contribution

It provides an experimental assessment of multiple algorithms for constructing STSs and introduces modifications to enhance their effectiveness across various sizes.

Findings

Algorithms' performance varies with system size

Occurrences of configurations align with hypergraph expectations

Proposed modifications improve algorithm outcomes

Abstract

Several methods for generating random Steiner triple systems (STSs) have been proposed in the literature, such as Stinson's hill-climbing algorithm and Cameron's algorithm, but these are not yet completely understood. Those algorithms, as well as some variants, are here assessed for STSs of both small and large orders. For large orders, the number of occurrences of certain configurations in the constructed STSs are compared with the corresponding expected values of random hypergraphs. Modifications of the algorithms are proposed.