FPT Inapproximability of Directed Cut and Connectivity Problems
Abstract
(see paper for full abstract) Cut problems and connectivity problems on digraphs are two well-studied classes of problems from the viewpoint of parameterized complexity. After a series of papers over the last decade, we now have (almost) tight bounds for the running time of several standard variants of these problems parameterized by two parameters: the number of terminals and the size of the solution. When there is evidence of FPT intractability, then the next natural alternative is to consider FPT approximations. In this paper, we show two types of results for several directed cut and connectivity problems, building on existing results from the literature: first is to circumvent the hardness results for these problems by designing FPT approximation algorithms, or alternatively strengthen the existing hardness results by creating "gap-instances" under stronger hypotheses such as the (Gap-)Exponential Time Hypothesis (ETH).
Cite
@article{arxiv.1910.01934,
title = {FPT Inapproximability of Directed Cut and Connectivity Problems},
author = {Rajesh Chitnis and Andreas Emil Feldmann},
journal= {arXiv preprint arXiv:1910.01934},
year = {2019}
}
Comments
Extended abstract in IPEC 2019. arXiv admin note: text overlap with arXiv:1707.06499