(In)approximability of maximum minimal FVS

Louis Dublois, Tesshu Hanaka, Mehdi Khosravian Ghadikolaei, Michael Lampis, Nikolaos Melissinos

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)


We study the approximability of the NP-complete Maximum Minimal Feedback Vertex Set problem. Informally, this natural problem seems to lie in an intermediate space between two more well-studied problems of this type: Maximum Minimal Vertex Cover, for which the best achievable approximation ratio is √n, and Upper Dominating Set, which does not admit any n1−∊ approximation. We confirm and quantify this intuition by showing the first non-trivial polynomial time approximation for Max Min FVS with a ratio of O(n2/3), as well as a matching hardness of approximation bound of n2/3−∊, improving the previous known hardness of n1/2−∊. Along the way, we also obtain an O(∆)-approximation and show that this is asymptotically best possible, and we improve the bound for which the problem is NP-hard from ∆ ≥ 9 to ∆ ≥ 6. Having settled the problem’s approximability in polynomial time, we move to the context of super-polynomial time. We devise a generalization of our approximation algorithm which, for any desired approximation ratio r, produces an r-approximate solution in time nO(n/r3/2). This time-approximation trade-off is essentially tight: we show that under the ETH, for any ratio r and ∊ > 0, no algorithm can r-approximate this problem in time nO((n/r3/2)1−∊), hence we precisely characterize the approximability of the problem for the whole spectrum between polynomial and sub-exponential time, up to an arbitrarily small constant in the second exponent.

Original languageEnglish
Title of host publication31st International Symposium on Algorithms and Computation, ISAAC 2020
EditorsYixin Cao, Siu-Wing Cheng, Minming Li
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Number of pages284
ISBN (Electronic)9783959771733
Publication statusPublished - Dec 2020
Externally publishedYes
Event31st International Symposium on Algorithms and Computation, ISAAC 2020 - Virtual, Hong Kong, China
Duration: Dec 14 2020Dec 18 2020

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference31st International Symposium on Algorithms and Computation, ISAAC 2020
CityVirtual, Hong Kong

All Science Journal Classification (ASJC) codes

  • Software


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