Complexity of constraint satisfaction Dissertation Thesis


Author(s): Rolinek, Michal
Advisor(s): Kolmogorov, Vladimir
Committee Chair(s): Lemeshko, Mikhail
Committee Member(s): Wagner, Uli; Krokhin, Andrei
Title: Complexity of constraint satisfaction
Affiliation IST Austria
Abstract: An instance of the Constraint Satisfaction Problem (CSP) is given by a finite set of variables, a finite domain of labels, and a set of constraints, each constraint acting on a subset of the variables. The goal is to find an assignment of labels to its variables that satisfies all constraints (or decide whether one exists). If we allow more general “soft” constraints, which come with (possibly infinite) costs of particular assignments, we obtain instances from a richer class called Valued Constraint Satisfaction Problem (VCSP). There the goal is to find an assignment with minimum total cost. In this thesis, we focus (assuming that P 6 = NP) on classifying computational com- plexity of CSPs and VCSPs under certain restricting conditions. Two results are the core content of the work. In one of them, we consider VCSPs parametrized by a constraint language, that is the set of “soft” constraints allowed to form the instances, and finish the complexity classification modulo (missing pieces of) complexity classification for analogously parametrized CSP. The other result is a generalization of Edmonds’ perfect matching algorithm. This generalization contributes to complexity classfications in two ways. First, it gives a new (largest known) polynomial-time solvable class of Boolean CSPs in which every variable may appear in at most two constraints and second, it settles full classification of Boolean CSPs with planar drawing (again parametrized by a constraint language).
Publication Title: IST Dissertation
Degree Granting Institution: IST Austria  
Degree Date: 2017-05-01
Start Page: 1
Total Pages: 97
Sponsor: FP7/2007-2013/ERC grant agreement no 616160
DOI: 10.15479/AT:ISTA:th_815
Open access: yes (repository)
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