Solving Systems of Difference Constraints Incrementally

G. Ramalingam, Junehwa Song, Leo Joskowicz, Raymond E. Miller

Abstract: Difference constraints systems consisting of inequalities of the form x i - x j \( \leq \) b i,j occur in many applications, most notably those involving temporal reasoning. Often, it is necessary to maintain a solution to such a system as constraints are added, modified, and deleted. Existing algorithms handle modifications by solving the resulting system anew each time, which is inefficient. The best known algorithm to determine if a system of difference constraints is feasible (i.e., if it has a solution) and to compute a solution runs in Θ (mn) time, where n is the number of variables and m is the number of constraints.