Random Constraint Satisfaction: Flaws and Structure

Research Report 98.23, School of Computer Studies, University of Leeds, October 1998.
Ian P Gent, Ewan MacIntyre, Patrick Prosser, Barbara M Smith and Toby Walsh

Abstract

A recent theoretical result by Achlioptas et al. shows that conventional models of random problems are trivially insoluble in the limit. This insolubility is due to the presence of `flawed variables', variables whose values are all `flawed' (or unsupported). We survey the literature to identify experimental studies that lie within the scope of this result. We then estimate theoretically and measure experimentally the size at which flawed variables can be expected to occur. We also study an alternative model of random problems proposed by Achlioptas et al. to tackle such flaws. We show that flawed values still occur in this model at problem sizes similar to those used in practice. To eliminate flawed values and variables, we introduce a `flawless' generator by putting a limited amount of structure into the conflict matrix. We also show how to introduce structure into the constraint graph. We can thereby generate ensembles of problems that are not trivially insoluble due to the presence of flawed variables, as well as problems that contain structures in their constraint graphs which are rare in purely random problems.

Back to "Barbara Smith - Publications on Constraint Programming"