Slim Tree-Cut Width

Tree-cut width is a parameter that has been introduced as an attempt to obtain an analogue of treewidth for edge cuts. Unfortunately, in spite of its desirable structural properties, it turned out that tree-cut width falls short as an edge-cut based alternative to treewidth in algorithmic aspects. T...

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Bibliographic Details
Published in:Algorithmica 2024, Vol.86 (8), p.2714-2738
Main Authors: Ganian, Robert, Korchemna, Viktoriia
Format: Article
Language:English
Subjects:
Algorithm Analysis and Problem Complexity
Algorithms
Computer Science
Computer Systems Organization and Communication Networks
Cut width
Data Structures and Information Theory
Decomposition
Mathematics of Computing
Parameters
Structural analysis
Theory of Computation
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Summary:Tree-cut width is a parameter that has been introduced as an attempt to obtain an analogue of treewidth for edge cuts. Unfortunately, in spite of its desirable structural properties, it turned out that tree-cut width falls short as an edge-cut based alternative to treewidth in algorithmic aspects. This has led to the very recent introduction of a simple edge-based parameter called edge-cut width [WG 2022], which has precisely the algorithmic applications one would expect from an analogue of treewidth for edge cuts, but does not have the desired structural properties. In this paper, we study a variant of tree-cut width obtained by changing the threshold for so-called thin nodes in tree-cut decompositions from 2 to 1. We show that this “slim tree-cut width” satisfies all the requirements of an edge-cut based analogue of treewidth, both structural and algorithmic, while being less restrictive than edge-cut width. Our results also include an alternative characterization of slim tree-cut width via an easy-to-use spanning-tree decomposition akin to the one used for edge-cut width, a characterization of slim tree-cut width in terms of forbidden immersions as well as approximation algorithm for computing the parameter.
ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-024-01241-4