An Algorithm for the Exact Treedepth Problem

Author James Trimble

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James Trimble
  • School of Computing Science, University of Glasgow, UK


Thanks to Ciaran McCreesh, David Manlove, Patrick Prosser and the anonymous referees for their helpful feedback, and to Robert Ganian, Neha Lodha, and Vaidyanathan Peruvemba Ramaswamy for providing software for the SAT encoding.

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James Trimble. An Algorithm for the Exact Treedepth Problem. In 18th International Symposium on Experimental Algorithms (SEA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 160, pp. 19:1-19:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


We present a novel algorithm for the minimum-depth elimination tree problem, which is equivalent to the optimal treedepth decomposition problem. Our algorithm makes use of two cheaply-computed lower bound functions to prune the search tree, along with symmetry-breaking and domination rules. We present an empirical study showing that the algorithm outperforms the current state-of-the-art solver (which is based on a SAT encoding) by orders of magnitude on a range of graph classes.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Algorithm design techniques
  • Treedepth
  • Elimination Tree
  • Graph Algorithms


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