Counting or producing all fixed cardinality transversals

TL;DR

This paper presents an algorithm for counting and generating all fixed-size transversals of a set system, with efficiency improvements for special cases, and compares it to existing methods.

Contribution

It introduces a new algorithm for fixed cardinality transversals that operates in output-linear time for certain cases and provides a comparative analysis.

Findings

Algorithm efficiently counts and generates transversals.

Works in output-linear time for special cases.

Compared favorably with existing methods.

Abstract

An algorith to count, or alternatively generate, all k-element transversals of a set system is presented and compared with three known methods. For special cases it works in output-linear time.