Cubic Time Recognition of Cocircuit Graphs of Uniform Oriented Matroids

TL;DR

This paper introduces a cubic time algorithm to recognize cocircuit graphs of uniform oriented matroids and retrieve their signed cocircuits, improving previous algorithms and strengthening related connectivity results.

Contribution

The authors develop a more efficient cubic time algorithm for recognizing cocircuit graphs and extracting cocircuits, advancing the computational understanding of uniform oriented matroids.

Findings

Algorithm operates in cubic time

Successfully identifies cocircuit graphs of uniform oriented matroids

Enhances previous recognition algorithms

Abstract

We present an algorithm which takes a graph as input and decides in cubic time if the graph is the cocircuit graph of a uniform oriented matroid. In the affirmative case the algorithm returns the set of signed cocircuits of the oriented matroid. This improves an algorithm proposed by Babson, Finschi and Fukuda. Moreover we strengthen a result of Montellano-Ballesteros and Strausz about crabbed connectivity of cocircuit graphs of uniform oriented matroids.