(In)approximability of maximum minimal FVS

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

Research output: Contribution to journalArticlepeer-review

Abstract

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−ϵ approximation. We confirm and quantify this intuition by showing the first non-trivial polynomial time approximation for MAXIMUM MINIMAL FEEDBACK VERTEX SET with a ratio of O(n2/3), as well as a matching hardness of approximation bound of n2/3−ϵ, improving the previously known hardness of n1/2−ϵ. 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 under the ETH.

Original languageEnglish
Pages (from-to)26-40
Number of pages15
JournalJournal of Computer and System Sciences
Volume124
DOIs
Publication statusPublished - Mar 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Networks and Communications
  • Computational Theory and Mathematics
  • Applied Mathematics

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