Algorithms for Media

TL;DR

This paper explores algorithmic solutions for media, a broad class of combinatorial structures, addressing problems like reset sequences, shortest paths, and state enumeration to enhance understanding and manipulation of these objects.

Contribution

It provides efficient algorithms for key problems on media, expanding computational tools for this general combinatorial framework.

Findings

Efficient algorithms for finding short reset sequences.

Methods for shortest path computation in media.

Techniques for listing states from black-box descriptions.

Abstract

Falmagne recently introduced the concept of a medium, a combinatorial object encompassing hyperplane arrangements, topological orderings, acyclic orientations, and many other familiar structures. We find efficient solutions for several algorithmic problems on media: finding short reset sequences, shortest paths, testing whether a medium has a closed orientation, and listing the states of a medium given a black-box description.