Parameterized complexity and approximability of directed odd cycle transversal

Daniel Lokshtanov, M. S. Ramanujan, Saket Saurabh, Meirav Zehavi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

13 Scopus citations

Abstract

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.

Original languageEnglish
Title of host publication31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020
EditorsShuchi Chawla
PublisherAssociation for Computing Machinery
Pages2181-2200
Number of pages20
ISBN (Electronic)9781611975994
StatePublished - 1 Jan 2020
Event31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020 - Salt Lake City, United States
Duration: 5 Jan 20208 Jan 2020

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Volume2020-January

Conference

Conference31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020
Country/TerritoryUnited States
CitySalt Lake City
Period5/01/208/01/20

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