@inproceedings{6725,
abstract = {A Valued Constraint Satisfaction Problem (VCSP) provides a common framework that can express a wide range of discrete optimization problems. A VCSP instance is given by a finite set of variables, a finite domain of labels, and an objective function to be minimized. This function is represented as a sum of terms where each term depends on a subset of the variables. To obtain different classes of optimization problems, one can restrict all terms to come from a fixed set Γ of cost functions, called a language.
Recent breakthrough results have established a complete complexity classification of such classes with respect to language Γ: if all cost functions in Γ satisfy a certain algebraic condition then all Γ-instances can be solved in polynomial time, otherwise the problem is NP-hard. Unfortunately, testing this condition for a given language Γ is known to be NP-hard. We thus study exponential algorithms for this meta-problem. We show that the tractability condition of a finite-valued language Γ can be tested in O(3‾√3|D|⋅poly(size(Γ))) time, where D is the domain of Γ and poly(⋅) is some fixed polynomial. We also obtain a matching lower bound under the Strong Exponential Time Hypothesis (SETH). More precisely, we prove that for any constant δ<1 there is no O(3‾√3δ|D|) algorithm, assuming that SETH holds.},
author = {Kolmogorov, Vladimir},
booktitle = {46th International Colloquium on Automata, Languages and Programming},
isbn = {978-3-95977-109-2},
issn = {1868-8969},
location = {Patras, Greece},
pages = {77:1--77:12},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Testing the complexity of a valued CSP language}},
doi = {10.4230/LIPICS.ICALP.2019.77},
volume = {132},
year = {2019},
}