Flexibility and decoupling in the simple temporal problem

In this paper we concentrate on finding a suitable metric to determine the flexibility of a Simple Temporal Problem (STP). After reviewing some flexibility metrics that have been proposed, we conclude that these metrics fail to capture the correlation between events specified in the STP, resulting in an overestimation of the available flexibility in the system. We propose to use an intuitively more acceptable flexibility metric based upon uncorrelated time-intervals for the allowed starting times of events in an STP. This metric is shown to be computable in low-polynomial time. As a byproduct of the flexibility computation, we get a decomposition of the STN almost for free: for every possible k-partitioning of the event space, a decomposition can be computed in O(k)-time. Even more importantly, we show that contrary to popular belief, such a decomposition does not affect the flexibility of the original STP.