Constraint satisfaction problems (CSP) form a general framework that captures a large variety of algorithmic problems. Due to their generality, CSPs are ubiquitous in several areas such as, for example, artificial intelligence, database theory and statistical physics. Therefore it is not surprising that their study is of prominent importance also in computational complexity theory. The proposed research aims at studying algorithmic issues related to CSPs from the perspective of computational complexity. The project consists of two parts.
Firstly, we intend to widen the current understanding of algorithmic approaches to solving CSPs with a particular focus on the propositional satisfiability problem SAT. Recent years have seen an immense increase in the efficiency of practical algorithms solving the propositional satisfiability problem - so-called SAT solvers. Today we still do only have a limited understanding of the reasons for this increase.
We will study these reasons. This will, among other things, include studying structural restrictions of input formulas which are likely to be relevant in practice. Along similar lines we will also examine the capabilities of other algorithmic approaches which are applicable to CSPs in general.
Secondly, we will study weighted extensions of CSPs from a structural point of view. Over the past few years, these versions of CSPs have received increased attention in the context of counting complexity. A main motivation for studying them arises from their connection to so-called spin glass models from statistical physics. Although we have a quite good understanding of the complexity of exactly computing them, we still have only little knowledge of the extent to which these weighted versions of CSPs can be approximated efficiently. The research project aims at extending this knowledge significantly.
Call for proposal
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