A 2-Approximation Algorithm for Feedback Vertex Set in Tournaments

Daniel Lokshtanov; Pranabendu Misra; Joydeep Mukherjee; Geevarghese Philip; Fahad Panolan; Saket Saurabh

A 2-Approximation Algorithm for Feedback Vertex Set in Tournaments

Data Structures and Algorithms 2018-09-25 v1

Authors: Daniel Lokshtanov , Pranabendu Misra , Joydeep Mukherjee , Geevarghese Philip , Fahad Panolan , Saket Saurabh

Abstract

A {\em tournament} is a directed graph $T$ such that every pair of vertices is connected by an arc. A {\em feedback vertex set} is a set $S$ of vertices in $T$ such that $T - S$ is acyclic. We consider the {\sc Feedback Vertex Set} problem in tournaments. Here the input is a tournament $T$ and a weight function $w : V(T) \rightarrow \mathbb{N}$ and the task is to find a feedback vertex set $S$ in $T$ minimizing $w(S) = \sum_{v \in S} w(v)$ . 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.

Keywords

game theory approximation algorithm

Cite

@article{arxiv.1809.08437,
  title  = {A 2-Approximation Algorithm for Feedback Vertex Set in Tournaments},
  author = {Daniel Lokshtanov and Pranabendu Misra and Joydeep Mukherjee and Geevarghese Philip and Fahad Panolan and Saket Saurabh},
  journal= {arXiv preprint arXiv:1809.08437},
  year   = {2018}
}

A 2-Approximation Algorithm for Feedback Vertex Set in Tournaments

Abstract

Keywords

Cite

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