Decomposing and Solving Timetabling Constraint Networks

Abstract

The binary version of the school timetabling (STT) problem is a real‐world example of a constraint network that includes only constraints of inequality. A new and useful representation for this real‐world problem, the STT_Grid, leads to a generic decomposition technique. The paper presents proofs of necessary and sufficient conditions for the existence of a solution to decomposed STT_Grids. The decomposition procedure is of low enough complexity to be practical for large problems, such as a real‐world high school.To test the decomposition approach, a typical high school was analyzed and used as a model for generating STT_Grids of various sizes. Experiments were conducted to test the difficulty of large STT networks and their solution by decomposition. The experimental results show that the decomposition procedure enables the solution of large STT_Grids (620 variables for a real school) in reasonable time. The constraint network of a typical STT_Grid is sparse and belongs to the class of easy problems. Still, due to the sizes of STTs, good constraint satisfaction problem search techniques (i.e., BackJumping and ForwardChecking) do not terminate in reasonable times for STT_Grids that are larger than 300 variables.