eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2022-09-01
79:1
79:14
10.4230/LIPIcs.ESA.2022.79
article
Computing Treedepth in Polynomial Space and Linear FPT Time
Nadara, Wojciech
1
Pilipczuk, Michał
1
Smulewicz, Marcin
1
Institute of Informatics, University of Warsaw, Poland
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^𝒪(d²)⋅n^𝒪(1) and the space usage is polynomial in n. Further, by allowing randomization, the time and space complexities can be improved to 2^𝒪(d²)⋅n and d^𝒪(1)⋅n, respectively. This improves upon the algorithm of Reidl et al. [ICALP 2014], which also has time complexity 2^𝒪(d²)⋅n, but uses exponential space.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol244-esa2022/LIPIcs.ESA.2022.79/LIPIcs.ESA.2022.79.pdf
treedepth
FPT
polynomial space