A Short Note on Relevant Cuts

TL;DR

This paper characterizes relevant cuts in graphs, linking them to minimum weight bases and specific DAG structures, and demonstrates improved enumeration methods through experimental evaluation.

Contribution

It introduces a new characterization of relevant cuts using Picard-Queyranne DAGs and accelerates their enumeration with experimental validation.

Findings

Characterization of relevant cuts via Picard-Queyranne DAGs

Enhanced algorithms for relevant cut enumeration

Experimental comparison showing improved performance

Abstract

The set of relevant cuts in a graph is the union of all minimum weight bases of the cut space. A cut is relevant if and only if it is the a minimum weight cut between two distinct vertices. Moreover, we give a characterization in terms of Picard-Queyranne Directed Acyclic Graphs that can be used to accelerate the enumeration of the relevant cuts. Finally, we perform an experimental evaluation by comparing with state-of-the-art algorithms.