Projects per year
Abstract
The constraint satisfaction problem (CSP) is a general problem central to computer science and artificial intelligence. Although the CSP is NPhard in general, considerable effort has been spent on identifying tractable subclasses. The main two approaches consider structural properties (restrictions on the hypergraph of constraint scopes) and relational properties (restrictions on the language of constraint relations). Recently, some authors have considered hybrid properties that restrict the constraint hypergraph and the relations simultaneously.
Our key contribution is the novel concept of a CSP pattern and classes of problems defined by forbidden patterns (which can be viewed as forbidding generic subproblems). We describe the theoretical framework which can be used to reason about classes of problems defined by forbidden patterns. We show that this framework generalises relational properties and allows us to capture known hybrid tractable classes.
Although we are not close to obtaining a dichotomy concerning the tractability of general forbidden patterns, we are able to make some progress in a special case: classes of problems that arise when we can only forbid binary negative patterns (generic subproblems in which only inconsistent tuples are specified). In this case we are able to characterise very large classes of tractable and NPhard forbidden patterns. This leaves the complexity of just one case unresolved and we conjecture that this last case is tractable.
Our key contribution is the novel concept of a CSP pattern and classes of problems defined by forbidden patterns (which can be viewed as forbidding generic subproblems). We describe the theoretical framework which can be used to reason about classes of problems defined by forbidden patterns. We show that this framework generalises relational properties and allows us to capture known hybrid tractable classes.
Although we are not close to obtaining a dichotomy concerning the tractability of general forbidden patterns, we are able to make some progress in a special case: classes of problems that arise when we can only forbid binary negative patterns (generic subproblems in which only inconsistent tuples are specified). In this case we are able to characterise very large classes of tractable and NPhard forbidden patterns. This leaves the complexity of just one case unresolved and we conjecture that this last case is tractable.
Original language  English 

Number of pages  30 
Journal  Journal of Artificial Intelligence Research 
Volume  45 
Publication status  Published  2012 
Fingerprint
Dive into the research topics of 'The tractability of CSP classes defined by forbidden patterns'. Together they form a unique fingerprint.Projects
 1 Finished

Heterogeneous and Permanent data
Buneman, P., Fan, W., Libkin, L. & Viglas, S.
1/03/08 → 29/02/12
Project: Research