A Short Note on Relevant Cuts
Nico Domschke, Thomas Gatter, Richard Golnik, Peter F. Stadler

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.
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Taxonomy
TopicsManufacturing Process and Optimization · Material Properties and Processing
