Final Report Summary - COMPLEXITY OF CSPS (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.
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.
