Variable ordering heuristics can have a profound eeect on the performance of backtracking search algorithms for constraint satisfaction problems. The smallest-remaining-domain heuristic is a commonly-used dynamic variable ordering heuristic, used in conjunction with algorithms such as forward checking which look ahead at the eeects of each variable… (More)
Randomly-generated constraint satisfaction problems go through a phase transition as the constraint tightness varies. Loose constraints give anèasy-soluble' region, where problems have many solutions and are almost always easy to solve. However, in this region, systematic search algorithms may occasionally encounter problems which are extremely expensive to… (More)
Many types of problem exhibit a phase transition as a problem parameter is varied, from a region where most problems are easy and soluble to a region where most problems are easy but insoluble. In the intervening phase transition region, the median problem dii-culty is greatest. However, occasional exceptionally hard problems (ehps) can be found in the easy… (More)
In this paper, we study two recently presented algorithms employing a \full look-ahead" strategy: MAC (Maintaining Arc Consistency); and the hybrid MAC-CBJ, which combines connict-directed backjumping capability with MAC. We observe their behaviour with respect to the phase transition properties of randomly-generated binary constraint satisfaction problems,… (More)
We give some dos and don'ts for those analysing algorithms experimentally. We illustrate these with many examples from our own research on the study of algorithms for NP-complete problems such as satissability and constraint satisfaction. Where we have not followed these maxims, we have suuered as a result.
Constraint satisfaction problems exhibit a phase transition as a problem parameter is varied, from a region where most problems are easy and soluble to a region where most problems are easy but insoluble. In the intervening phase transition region, the median problem diiculty is greatest. However, in the easy and soluble region, occasional exceptionally… (More)
Phase transition behaviour has been observed in many classes of problem as a control parameter is varied, prompting a urry of research activity in recent years. This work has generally concentrated on the phase transitions found when searching problems for solutions, which occur between regions where most problems are easy to solve and regions where most… (More)