Results

**1 - 2**of**2**### Generating Custom Propagators for Arbitrary Constraints

"... Constraint Programming (CP) is a proven set of techniques for solving complex combinatorial problems from a range of disciplines. The problem is specified as a set of decision variables (with finite domains) and constraints linking the variables. Local reasoning (propagation) on the constraints is c ..."

Abstract
- Add to MetaCart

(Show Context)
Constraint Programming (CP) is a proven set of techniques for solving complex combinatorial problems from a range of disciplines. The problem is specified as a set of decision variables (with finite domains) and constraints linking the variables. Local reasoning (propagation) on the constraints is central to CP. Many constraints have efficient constraint-specific propagation algorithms. In this work, we generate custom propagators for constraints. These custom prop-agators can be very efficient, even approaching (and in some cases exceeding) the efficiency of hand-optimised propagators. Given an arbitrary constraint, we show how to generate a custom propagator that establishes GAC in small polynomial time. This is done by precomputing the propagation that would be performed on every relevant subdomain. The number of relevant subdomains, and therefore the size of the generated propaga-tor, is potentially exponential in the number and domain size of the constrained variables. The limiting factor of our approach is the size of the generated propagators. We investigate symmetry as a means of reducing that size. We exploit the sym-metries of the constraint to merge symmetric parts of the generated propagator. This extends the reach of our approach to somewhat larger constraints, with a small run-time penalty. Our experimental results show that, compared with optimised implementa-tions of the table constraint, our techniques can lead to an order of magnitude speedup. Propagation is so fast that the generated propagators compare well with hand-written carefully optimised propagators for the same constraints, and the time taken to generate a propagator is more than repaid.

### Exponential Propagation for Set-CSPs

"... Abstract. Research on constraint propagation has primarily focused on designing polynomial-time propagators sometimes at the cost of a weaker filtering. Interestingly, the evolution of constraint programming over sets have been diametrically different. The domain representations are becoming increas ..."

Abstract
- Add to MetaCart

(Show Context)
Abstract. Research on constraint propagation has primarily focused on designing polynomial-time propagators sometimes at the cost of a weaker filtering. Interestingly, the evolution of constraint programming over sets have been diametrically different. The domain representations are becoming increasingly expensive computationally and theoretical results appear to question the wisdom of these research directions. This paper explores this apparent contradiction by pursuing even more complexity in the domain representation and the filtering algorithms. It shows that the product of the length-lex and subset-bound domains improves filtering and produces orders of magnitude improvements over existing approaches on standard benchmarks. Moreover, the paper proposes exponential-time algorithms for NP-hard intersection constraints and demonstrates that they bring significant performance improvements and speeds up constraint propagation considerably. 1