Converting Simple Temporal Networks with Uncertainty into Minimal Equivalent Dispatchable Form

Luke Hunsberger, Roberto Posenato

Keywords: simple temporal networks with uncertainty, dynamic controllability, dispatchability

TL;DR: A new polynomial-time algorithm to convert any dispatchable STNU into an equivalent dispatchable network having a minimal number of edges.

Abstract:

A Simple Temporal Network with Uncertainty (STNU) is a structure
for representing and reasoning about time constraints on actions that
may have uncertain durations.
An STNU is dynamically controllable (DC) if there exists a dynamic strategy
for executing the network that guarantees that all of its constraints will be satisfied
no matter how the uncertain durations turn out---within their specified bounds.
However, such strategies typically require exponential space.
Therefore, converting a DC STNU into a so-called dispatchable form
for practical applications is essential.
The relevant portions of a real-time execution strategy for a dispatchable
STNU can be incrementally constructed during execution, requiring only $O(n^2)$ space,
while also providing maximum flexibility and minimal computation during the execution
of the network.
Although existing algorithms can generate equivalent-dispatchable STNUs,
they do not guarantee a minimal number of edges in the STNU graph.
Since the number of edges directly impacts the computations during execution, this paper
presents a novel algorithm for converting any dispatchable STNU into
an equivalent dispatchable network having a minimal number of edges.
The complexity of the algorithm is $O(kn^3)$, where $k$ is the number of actions with uncertain durations,
and $n$ is the number of timepoints in the network.
The paper also provides an empirical evaluation of the reduction of edges obtained by the impact of the new algorithm.

Primary Keywords: Temporal Planning

Category: Long

Student: No

Submission Number: 66