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 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 …

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 …

The complexity of adversarially robust proper learning of halfspaces with agnostic noise

I Diakonikolas, DM Kane… - Advances in Neural …, 2020 - proceedings.neurips.cc
We study the computational complexity of adversarially robust proper learning of halfspaces
in the distribution-independent agnostic PAC model, with a focus on $ L_p $ perturbations …

Flow-augmentation III: Complexity dichotomy for Boolean CSPs parameterized by the number of unsatisfied constraints

EJ Kim, S Kratsch, M Pilipczuk, M Wahlström - … of the 2023 Annual ACM-SIAM …, 2023 - SIAM
We study the parameterized problem of satisfying “almost all” constraints of a given formula
F over a fixed, finite Boolean constraint language Γ, with or without weights. More precisely …

Almost polynomial factor inapproximability for parameterized k-clique

CS Karthik, S Khot - 37th Computational Complexity Conference …, 2022 - drops.dagstuhl.de
The k-Clique problem is a canonical hard problem in parameterized complexity. In this
paper, we study the parameterized complexity of approximating the k-Clique problem where …

Solving hard cut problems via flow-augmentation

EJ Kim, S Kratsch, M Pilipczuk, M Wahlström - Proceedings of the 2021 ACM …, 2021 - SIAM
We present a new technique for designing fixed-parameter algorithms for graph cut
problems in undirected graphs, which we call flow augmentation. Our technique is …

Parameterized Inapproximability of the Minimum Distance Problem over All Fields and the Shortest Vector Problem in All ℓp Norms

H Bennett, M Cheraghchi, V Guruswami… - Proceedings of the 55th …, 2023 - dl.acm.org
We prove that the Minimum Distance Problem (MDP) on linear codes over any fixed finite
field and parameterized by the input distance bound is W [1]-hard to approximate within any …

The complexity of the shortest vector problem

H Bennett - ACM SIGACT News, 2023 - dl.acm.org
Computational problems on point lattices play a central role in many areas of computer
science including integer programming, coding theory, cryptanalysis, and especially the …

The complexity of valued CSPs

A Krokhin, S Zivny - 2017 - drops.dagstuhl.de
We survey recent results on the broad family of problems that can be cast as valued
constraint satisfaction problems (VCSPs). We discuss general methods for analysing the …