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PACE Solver Description: Sallow: A Heuristic Algorithm for Treedepth Decompositions

Author Marcin Wrochna

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Marcin Wrochna
  • University of Oxford, UK


The author is very grateful to the organizers at the University of Warsaw, organizers of past editions, and the team at the Poznań University of Technology for making this challenge possible.

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Marcin Wrochna. PACE Solver Description: Sallow: A Heuristic Algorithm for Treedepth Decompositions. In 15th International Symposium on Parameterized and Exact Computation (IPEC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 180, pp. 36:1-36:4, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


We describe a heuristic algorithm for computing treedepth decompositions, submitted for the challenge. It relies on a variety of greedy algorithms computing elimination orderings, as well as a Divide & Conquer approach on balanced cuts obtained using a from-scratch reimplementation of the 2016 FlowCutter algorithm by Hamann & Strasser [Michael Hamann and Ben Strasser, 2018].

Subject Classification

ACM Subject Classification
  • Theory of computation → Discrete optimization
  • Mathematics of computing → Solvers
  • Mathematics of computing → Graph theory
  • treedepth
  • decomposition
  • heuristic
  • weak colouring numbers


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  2. Michael Hamann and Ben Strasser. Graph bisection with pareto optimization. ACM Journal of Experimental Algorithmics, 23, 2018. URL:
  3. Jaroslav Nešetřil and Patrice Ossona de Mendez. Bounded height trees and tree-depth. In Sparsity, pages 115-144. Springer, 2012. URL:
  4. Ben Strasser. Computing tree decompositions with flowcutter: PACE 2017 submission. CoRR, abs/1709.08949, 2017. URL:
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  6. Jan van den Heuvel, Patrice Ossona de Mendez, Daniel Quiroz, Roman Rabinovich, and Sebastian Siebertz. On the generalised colouring numbers of graphs that exclude a fixed minor. Eur. J. Comb., 66:129-144, 2017. URL:
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