License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2022.79
URN: urn:nbn:de:0030-drops-170175
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Nadara, Wojciech ; Pilipczuk, Michał ; Smulewicz, Marcin

Computing Treedepth in Polynomial Space and Linear FPT Time

LIPIcs-ESA-2022-79.pdf (0.9 MB)


The treedepth of a graph G is the least possible depth of an elimination forest of G: a rooted forest on the same vertex set where every pair of vertices adjacent in G is bound by the ancestor/descendant relation. We propose an algorithm that given a graph G and an integer d, either finds an elimination forest of G of depth at most d or concludes that no such forest exists; thus the algorithm decides whether the treedepth of G is at most d. The running time is 2^?(d²)⋅n^?(1) and the space usage is polynomial in n. Further, by allowing randomization, the time and space complexities can be improved to 2^?(d²)⋅n and d^?(1)⋅n, respectively. This improves upon the algorithm of Reidl et al. [ICALP 2014], which also has time complexity 2^?(d²)⋅n, but uses exponential space.

BibTeX - Entry

  author =	{Nadara, Wojciech and Pilipczuk, Micha{\l} and Smulewicz, Marcin},
  title =	{{Computing Treedepth in Polynomial Space and Linear FPT Time}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{79:1--79:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-170175},
  doi =		{10.4230/LIPIcs.ESA.2022.79},
  annote =	{Keywords: treedepth, FPT, polynomial space}

Keywords: treedepth, FPT, polynomial space
Collection: 30th Annual European Symposium on Algorithms (ESA 2022)
Issue Date: 2022
Date of publication: 01.09.2022

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