2-Approximating Feedback Vertex Set in Tournaments

被引：0

作者：

Lokshtanov, Daniel ^{[1
]}

Misra, Pranabendu ^{[2
]}

Mukherjee, Joydeep ^{[3
,4
]}

Panolan, Fahad ^{[5
]}

Philip, Geevarghese ^{[6
,7
]}

Saurabh, Saket ^{[7
,8
,9
]}

机构：

[1] Univ Calif Santa Barbara, Santa Barbara, CA 93106 USA

[2] Max Planck Inst Informat, Saarbrucken, Germany

[3] Indian Stat Inst, Kolkata, India

[4] Ramakrishna Mission Vivekananda Educ & Res Inst, Kolkata, India

[5] Indian Inst Technol, Hyderabad, India

[6] Chennai Math Inst, Chennai, Tamil Nadu, India

[7] IRL 2000 ReLaX, Chennai, Tamil Nadu, India

[8] HBNI, Inst Math Sci, Chennai, Tamil Nadu, India

[9] Univ Bergen, Bergen, Norway

来源：

PROCEEDINGS OF THE THIRTY-FIRST ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS (SODA'20) | 2020年

基金：

欧洲研究理事会;

关键词：

APPROXIMATION ALGORITHM;

D O I：

暂无

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

A tournament is a directed graph T such that every pair of vertices is connected by an arc. A feedback vertex set is a set S of vertices in T such that T - S is acyclic. We consider the FEEDBACK VERTEX SET problem in tournaments. Here the input is a tournament T and a weight function w : V(T) -> N and the task is to find a feedback vertex set S in T minimizing w(S) = Sigma(v is an element of S) w(v). Rounding optimal solutions to the natural LP-relaxation of this problem yields a simple 3-approximation algorithm. This has been improved to 2.5 by Cai et al. [SICOMP 2000], and subsequently to 7/3 by Mnich et al. [ESA 2016]. In this paper we give the first polynomial time factor 2 approximation algorithm for this problem. Assuming the Unique Games conjecture, this is the best possible approximation ratio achievable in polynomial time.

引用

页码：1010 / 1018

页数：9

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