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# A Linear Time Algorithm for the k-Cutset Constraint

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LIPIcs.CP.2021.29.pdf
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## Cite As

Nicolas Isoart and Jean-Charles Régin. A Linear Time Algorithm for the k-Cutset Constraint. In 27th International Conference on Principles and Practice of Constraint Programming (CP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 210, pp. 29:1-29:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.CP.2021.29

## Abstract

In CP, the most efficient model solving the TSP is the Weighted Circuit Constraint (WCC) combined with the k-cutset constraint. The WCC is mainly based on the edges cost of a given graph whereas the k-cutset constraint is a structural constraint. Specifically, for each cutset in a graph, the k-cutset constraint imposes that the size of the cutset is greater than or equal to two. In addition, any solution contains an even number of elements from this cutset. Isoart and Régin introduced an algorithm for this constraint. Unfortunately, their approach leads to a time complexity growing with the size of the considered cutsets, i.e. with k. Thus, they introduced an algorithm with a quadratic complexity dealing with k lower or equal to three. In this paper, we introduce a linear time algorithm for any k based on a DFS checking the consistency of this constraint and performing its filtering. Experimental results show that the size of most of the k-cutsets is lower or equal than 3. In addition, since the time complexity is improved, our algorithm also improves the solving times.

## Subject Classification

##### ACM Subject Classification
• Theory of computation → Constraint and logic programming
##### Keywords
• k-Cutset
• TSP
• Linear algorithm
• Constraint

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