A survey on approximation in parameterized complexity: Hardness and algorithms

AE Feldmann, E Lee, P Manurangsi - Algorithms, 2020 - mdpi.com
Parameterization and approximation are two popular ways of coping with NP-hard
problems. More recently, the two have also been combined to derive many interesting …

Tight FPT Approximations for -Median and -Means

V Cohen-Addad, A Gupta, A Kumar, E Lee… - arXiv preprint arXiv …, 2019 - arxiv.org
We investigate the fine-grained complexity of approximating the classical $ k $-median/$ k $-
means clustering problems in general metric spaces. We show how to improve the …

On the parameterized complexity of approximating dominating set

CS Karthik, B Laekhanukit… - 50th Annual ACM …, 2018 - weizmann.elsevierpure.com
We study the parameterized complexity of approximating the kDominating Set (DomSet)
problem where an integer k and a graph G on n vertices are given as input, and the goal is …

Independent Set on -Free Graphs in Quasi-Polynomial Time

P Gartland, D Lokshtanov - 2020 IEEE 61st Annual Symposium …, 2020 - ieeexplore.ieee.org
We present an algorithm that takes as input a graph G with weights on the vertices, and
computes a maximum weight independent set S of G. If the input graph G excludes a path P …

Tight hardness results for training depth-2 ReLU networks

S Goel, A Klivans, P Manurangsi… - arXiv preprint arXiv …, 2020 - arxiv.org
We prove several hardness results for training depth-2 neural networks with the ReLU
activation function; these networks are simply weighted sums (that may include negative …

Substroke approach to HMM-based on-line Kanji handwriting recognition

M Nakai, N Akira, H Shimodaira… - Proceedings of Sixth …, 2001 - ieeexplore.ieee.org
A new method is proposed for online handwriting recognition of Kanji characters. The
method employs substroke HMM as minimum units to constitute Japanese Kanji characters …

Tight Running Time Lower Bounds for Strong Inapproximability of Maximum k-Coverage, Unique Set Cover and Related Problems (via t-Wise Agreement Testing …

P Manurangsi - Proceedings of the Fourteenth Annual ACM-SIAM …, 2020 - SIAM
We show, assuming the (randomized) Gap Exponential Time Hypothesis (Gap-ETH), that
the following tasks cannot be done in T (k)· N o (k)-time for any function T where N denote …

The strongish planted clique hypothesis and its consequences

P Manurangsi, A Rubinstein, T Schramm - arXiv preprint arXiv:2011.05555, 2020 - arxiv.org
We formulate a new hardness assumption, the Strongish Planted Clique Hypothesis
(SPCH), which postulates that any algorithm for planted clique must run in time $ n^{\Omega …

Parameterized complexity and approximability of directed odd cycle transversal

D Lokshtanov, MS Ramanujan, S Saurab… - Proceedings of the …, 2020 - SIAM
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) …

FPT-approximation for FPT problems

D Lokshtanov, P Misra, MS Ramanujan… - Proceedings of the 2021 …, 2021 - SIAM
Over the past decade, many results have focused on the design of parameterized
approximation algorithms for W [1]-hard problems. However, there are fundamental …