Temporal Flexibility Revisited: Maximizing Flexibility by Computing Bipartite Matchings

Book One

Volume

Proceedings of the International Conference on Automated Planning and Scheduling, 25

Technical Papers

We discuss two flexibility metrics for Simple Temporal Networks (STNs): the so-called naive flexibility metric based on the difference between earliest and latest starting times of temporal variables, and a recently proposed concurrent flexibility metric. We establish an interesting connection between the computation of these flexibility metrics and properties of the minimal distance matrix DS of an STN S: the concurrent flexibility metric can be computed by finding a minimum weight matching of a weighted bipartite graph completely specified by DS, while the naive flexibility metric corresponds to computing a maximum weight matching in the same graph. From a practical point of view this correspondence offers an advantage: instead of using an O(n5) LP-based approach, reducing the problem to a matching problem we derive an O(n3) algorithm for computing the concurrent flexibility metric.

10.1609/icaps.v25i1.13720