A Faster Algorithm for Converting Simple Temporal Networks with Uncertainty into Dispatchable Form

A Simple Temporal Network with Uncertainty (STNU) is a data structure for reasoning about time constraints on actions that may have uncertain durations. An STNU is dispatchable if it can be executed in real-time with minimal computation 1) satisfying all constraints no matter how the uncertain durations play out and 2) retaining maximum flexibility. The fastest known algorithm for converting STNUs into dispatchable form runs in O(n^3) time, where n is the number of timepoints. This paper presents a faster algorithm that runs in O(mn + kn^2 + n^2 log n) time, where m is the number of edges and k is the number of uncertain durations. This performance is particularly meaningful in fields like Business Process Management, where sparse STNUs can represent temporal processes or plans. For sparse STNUs, our algorithm generates dispatchable forms in O(n^2 log n) time , a significant improvement over the O(n^3)-time previous fastest algorithm.