Professor Andrei Krokhin's Outputs (7)

The approximability of MAX CSP with fixed-value constraints (2008)
Journal Article
Deineko, V., Jonsson, P., Klasson, M., & Krokhin, A. (2008). The approximability of MAX CSP with fixed-value constraints. Journal of the ACM, 55(4), Article 16. https://doi.org/10.1145/1391289.1391290

In the maximum constraint satisfaction problem (MAX CSP), one is given a finite collection of (possibly weighted) constraints on overlapping sets of variables, and the goal is to assign values from a given finite domain to the variables so as to maxi... Read More about The approximability of MAX CSP with fixed-value constraints.

Computational complexity of auditing finite attributes in statistical databases (2008)
Journal Article
Jonsson, P., & Krokhin, A. (2008). Computational complexity of auditing finite attributes in statistical databases. Journal of Computer and System Sciences, 74(5), 898-909. https://doi.org/10.1016/j.jcss.2008.02.002

We study the computational complexity of auditing finite attributes in databases allowing statistical queries. Given a database that supports statistical queries, the auditing problem is to check whether an attribute can be completely determined or n... Read More about Computational complexity of auditing finite attributes in statistical databases.

Retractions onto series-parallel posets (2008)
Journal Article
Dalmau, V., Krokhin, A., & Larose, B. (2008). Retractions onto series-parallel posets. Discrete Mathematics, 308(11), 2104-2114. https://doi.org/10.1016/j.disc.2006.08.010

The poset retraction problem for a poset P is whether a given poset Q containing P as a subposet admits a retraction onto P, that is, whether there is a homomorphism from Q onto P which fixes every element of P. We study this problem for finite serie... Read More about Retractions onto series-parallel posets.

Majority constraints have bounded pathwidth duality (2008)
Journal Article
Dalmau, V., & Krokhin, A. (2008). Majority constraints have bounded pathwidth duality. European Journal of Combinatorics, 29(4), 821-837. https://doi.org/10.1016/j.ejc.2007.11.020

We study certain constraint satisfaction problems which are the problems of deciding whether there exists a homomorphism from a given relational structure to a fixed structure with a majority polymorphism. We show that such a problem is equivalent to... Read More about Majority constraints have bounded pathwidth duality.

Maximizing supermodular functions on product lattices, with application to maximum constraint satisfaction (2008)
Journal Article
Krokhin, A., & Larose, B. (2008). Maximizing supermodular functions on product lattices, with application to maximum constraint satisfaction. SIAM Journal on Discrete Mathematics, 22(1), 312-328. https://doi.org/10.1137/060669565

Recently, a strong link has been discovered between supermodularity on lattices and tractability of optimization problems known as maximum constraint satisfaction problems. This paper strengthens this link. We study the problem of maximizing a superm... Read More about Maximizing supermodular functions on product lattices, with application to maximum constraint satisfaction.

Complexity of clausal constraints over chains (2008)
Journal Article
Creignou, N., Hermann, M., Krokhin, A., & Salzer, G. (2008). Complexity of clausal constraints over chains. Theory of Computing Systems, 42(2), 239-255. https://doi.org/10.1007/s00224-007-9003-z

We investigate the complexity of the satisfiability problem of constraints over finite totally ordered domains. In our context, a clausal constraint is a disjunction of inequalities of the form x≥d and x≤d. We classify the complexity of constraints b... Read More about Complexity of clausal constraints over chains.

Dualities for constraint satisfaction problems (2008)
Book Chapter
Bulatov, A., Krokhin, A., & Larose, B. (2008). Dualities for constraint satisfaction problems. In N. Creignou, P. Kolaitis, & H. Vollmer (Eds.), Complexity of constraints : an overview of current research themes (93-124). Springer Verlag. https://doi.org/10.1007/978-3-540-92800-3_5

In a nutshell, a duality for a constraint satisfaction problem equates the existence of one homomorphism to the non-existence of other homomorphisms. In this survey paper, we give an overview of logical, combinatorial, and algebraic aspects of the fo... Read More about Dualities for constraint satisfaction problems.