TY - GEN

T1 - Parameterized complexity and approximability of directed odd cycle transversal

AU - Lokshtanov, Daniel

AU - Ramanujan, M. S.

AU - Saurabh, Saket

AU - Zehavi, Meirav

N1 - Publisher Copyright:
Copyright © 2020 by SIAM

PY - 2020/1/1

Y1 - 2020/1/1

N2 - A directed odd cycle transversal of a directed graph (digraph) D is a vertex set S that intersects every odd directed cycle of D. In the Directed Odd Cycle Transversal (DOCT) problem, the input consists of a digraph D and an integer k. The objective is to determine whether there exists a directed odd cycle transversal of D of size at most k. In this paper, we settle the parameterized complexity of DOCT when parameterized by the solution size k by showing that DOCT does not admit an algorithm with running time f(k)nO(1) unless FPT = W[1]. On the positive side, we give a factor 2 fixed-parameter approximation (FPT approximation) algorithm for the problem. More precisely, our algorithm takes as input D and k, runs in time 2O(k2)nO(1), and either concludes that D does not have a directed odd cycle transversal of size at most k, or produces a solution of size at most 2k. Finally, assuming gap-ETH, we show that there exists an ε > 0 such that DOCT does not admit a factor (1 + ε) FPT-approximation algorithm.

AB - A directed odd cycle transversal of a directed graph (digraph) D is a vertex set S that intersects every odd directed cycle of D. In the Directed Odd Cycle Transversal (DOCT) problem, the input consists of a digraph D and an integer k. The objective is to determine whether there exists a directed odd cycle transversal of D of size at most k. In this paper, we settle the parameterized complexity of DOCT when parameterized by the solution size k by showing that DOCT does not admit an algorithm with running time f(k)nO(1) unless FPT = W[1]. On the positive side, we give a factor 2 fixed-parameter approximation (FPT approximation) algorithm for the problem. More precisely, our algorithm takes as input D and k, runs in time 2O(k2)nO(1), and either concludes that D does not have a directed odd cycle transversal of size at most k, or produces a solution of size at most 2k. Finally, assuming gap-ETH, we show that there exists an ε > 0 such that DOCT does not admit a factor (1 + ε) FPT-approximation algorithm.

UR - http://www.scopus.com/inward/record.url?scp=85084091726&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85084091726

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 2181

EP - 2200

BT - 31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020

A2 - Chawla, Shuchi

PB - Association for Computing Machinery

T2 - 31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020

Y2 - 5 January 2020 through 8 January 2020

ER -