Complexity of CSPs · Algorithms and Complexity of Constraint Satisfaction Problems
FP7 — People (Marie Curie Actions)
- Duration
- 2011-04-01 → 2012-03-31
- EU contribution
- €159,866
- Participants
- 1
- Scheme
- MC-IEF
Lines connect the coordinator with its partners.
Results in brief
Algorithms and Complexity of Constraint Satisfaction Problems
This is a summary of the results of the research project COMPLEXITY OF CSPS. For background and further details on each topic I refer to my research proposal. Following this proposal, my main aim has been the study of the efficient approximability of counting problems in constraint satisfaction (#CSP). A second line of research was related to the investigation of resource bounded resolution. After the first few months of work on this topic, however, I saw a need to adapt my work plan. New publications - to be discussed below - implied tremendous progress on several problems related to the second part of my research proposal. This progress made by other research groups necessitated a stronger focus on that second part, as further efforts by these other groups became more likely. After the first three months of the project, I therefore focused exclusively on the topics #BIS and 'homomorphism functions' that can be found in my working plan under II.1 and II.2. For convenience, I provide here a short list containing the objectives met so far. The numbers indicate milestones from my proposal. I.1 Resolution: Ruled out the applicability of several lower bound techniques. II.1 #BIS: Determined implications of the connection between #BIS and linear datalog. II.2 Homomorphism functions: Developed new algorithms, the results have been published.
Data: CORDIS, © European Union
Project objective
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.
Original text from CORDIS.
Participants
- Consorci Centre de Recerca Matematica · BellaterraCoordinatorSpain
Links
Data: CORDIS, © European Union