Propagating Piecewise-Linear Weights in Temporal Networks

This paper presents a novel technique using piecewise-linear functions (PLFs) as weights on edges in the graphs of two kinds of temporal networks to solve several previously open problems. Generalizing constraint-propagation rules to accom- modate PLF weights requires implementing a small handful of functions. Most problems are solved by inserting one or more edges with an initial weight of \u3b4 (a variable), then using the modified rules to propagate the PLF weights. For one kind of network, a new set of propagation rules is introduced to avoid a non-termination issue that arises when propagating PLF weights. The paper also presents two new results for determining the tightest horizon that can be imposed while preserving a network\u2019s dynamic consistency/controllability

A note on speeding up DC-checking for STNUs

A Simple Temporal Network with Uncertainty (STNU) includes real-valued variables, called time-points; binary difference constraints on those time-points; and contingent links that represent actions with uncertain durations. The most important property of an STNU is called dynamic controllability (DC); and algorithms for checking this property are called DC-checking algorithms. The DC-checking algorithm for STNUs with the best worst-case time-complexity is the RUL$^-$ algorithm due to Cairo, Hunsberger and Rizzi. Its complexity is $O(mn + k^2n + knlog n)$, where $n$ is the number of time-points, $m$ is the number of constraints (equivalently, the number of edges in the STNU graph), and $k$ is the number of contingent links. It is expected that this worst-case complexity cannot be improved upon. However, this paper provides a new implementation of the algorithm that improves its performance in practice by an order of magnitude, as demonstrated by a thorough empirical evaluation