TY - JOUR

T1 - (In)approximability of maximum minimal FVS

AU - Dublois, Louis

AU - Hanaka, Tesshu

AU - Khosravian Ghadikolaei, Mehdi

AU - Lampis, Michael

AU - Melissinos, Nikolaos

N1 - Funding Information:
This work is partially supported by PRC CNRS JSPS project PARAGA (Parameterized Approximation Graph Algorithms) JPJSBP 120192912 and by JSPS KAKENHI Grant Number JP19K21537 , JP21K17707 .
Publisher Copyright:
© 2021 Elsevier Inc.

PY - 2022/3

Y1 - 2022/3

N2 - 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.

AB - 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.

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U2 - 10.1016/j.jcss.2021.09.001

DO - 10.1016/j.jcss.2021.09.001

M3 - Article

AN - SCOPUS:85116167162

VL - 124

SP - 26

EP - 40

JO - Journal of Computer and System Sciences

JF - Journal of Computer and System Sciences

SN - 0022-0000

ER -