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Computing Shrub-Depth Decompositions

Authors Jakub Gajarský, Stephan Kreutzer

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Author Details

Jakub Gajarský
  • Technical University Berlin, Germany
Stephan Kreutzer
  • Technical University Berlin, Germany


We want to thank Sang-il Oum for suggesting that our techniques may be used to obtain the results of Section 6.

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Jakub Gajarský and Stephan Kreutzer. Computing Shrub-Depth Decompositions. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 56:1-56:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


Shrub-depth is a width measure of graphs which, roughly speaking, corresponds to the smallest depth of a tree into which a graph can be encoded. It can be thought of as a low-depth variant of clique-width (or rank-width), similarly as treedepth is a low-depth variant of treewidth. We present an fpt algorithm for computing decompositions of graphs of bounded shrub-depth. To the best of our knowledge, this is the first algorithm which computes the decomposition directly, without use of rank-width decompositions and FO or MSO logic.

Subject Classification

ACM Subject Classification
  • Theory of computation → Fixed parameter tractability
  • Mathematics of computing → Combinatorial algorithms
  • shrub-depth
  • tree-model
  • decomposition
  • fixed-parameter tractability


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