A Symbolic Approach to Interval Constraint Problems

We report on a symbolic approach to solving constraint problems, which uses relation algebra. The method gives good results for problems with constraints that are relations on intervals. Problems of up to 500 variables may be solved in expected cubic time. Strong evidence is presented that signi cant backtracking on random problems occurs only in the range 6 n:c 15, for c 0:5, where n is the number of variables, and c is the ratio of non-trivial constraints to possible constraints in the problem. Space performance of the method is a ected by the branching factor during search, and time performance by path-consistency calculations, including the calculation of compositions of relations.