Faster Conflict Generation for Dynamic Controllability

Abstract

In this paper, we focus on speeding up the temporal plan relaxation problem for dynamically controllable systems. We take a look at the current bestknown algorithm for determining dynamic controllability and augment it to efficiently generate conflicts when the network is deemed uncontrollable. Our work preserves the O(n 3 ) runtime of the best available dynamic controllability checker and improves on the previous best runtime of O(n 4 ) for extracting dynamic controllability conflicts. We then turn our attention to temporal plan relaxation tasks and show how we can leverage our work on conflicts and the structure of the network to efficiently make incremental updates intended to restore dynamic controllability by relaxing constraints. Our new algorithm, RELAXIDC, has the same asymptotic runtime as previous algorithms but sees dramatic empirical improvements over the course of repeated dynamic controllability checks.

Quantifying Degrees of Controllability in Temporal Networks with Uncertainty

“…Note that in our framework, we assume agents in networks are mandated to satisfy all requirement constraints, so that violating any one constraint is just as bad as violating all constraints simultaneously. This is consistent with the methodology of Yu, Fang, and Williams (2015), but contrasts with previous work (Cui et al 2015;Yu, Fang, and Williams 2014;Bhargava, Vaquero, and Williams 2017) that allows both requirement and contingent constraints to be relaxed, and research (Rossi, Venable, and Yorke-Smith 2003) that maximizes the number of constraints satisfied under preference schemes.…”

“…We used this definition in the cases of strong and dynamic controllability to produce the Degree of Strong Controllability (DSC) and the Degree of Dynamic Controllability (DDC) metrics, which provide information on the maximum probability of success using certain types of offline and online strategies respectively. In doing so, we found an efficient LP for approximating DSC, presented a locally optimal solution to a variant of the relaxation problem discussed by Bhargava, Vaquero, and Williams (2017), and provided a normal approximation method for estimating DDC. These contributions present a unified, geometric way of tracking the robustness of networks in the context of controllability.…”

“…Previous work characterized conflicts as a special type of negative cycle occurring in the labeled distance graph of an STNU (Morris 2006). Bhargava, Vaquero, and Williams (2017) built off this work and introduced a cubic algorithm to extract conflicts from networks. They identified conflicts with the aim of solving temporal relaxation problems.…”

“…Our approach tackles a specific variant of their general formulation, but in this special case obtains an analytic solution that is provably, locally optimal and can be computed in O(p log p) time for an STN with p conflicts. Moreover, ODC-RELAX can naturally be used as a subroutine in the conflict-directed search methods in (Yu, Fang, and Williams 2014) and the RELAXSEARCH method of Bhargava, Vaquero, and Williams (2017) to augment existing algorithms.…”

Dynamic Controllability of Controllable Conditional Temporal Problems with Uncertainty

“…Yu et al (2014) solved an LP over constraints of form (7) to find a single relaxation. Bhargava, Vaquero, and Williams (2017) enhanced the conflict exploration process by using an incremental method. However, provided we find all conflicts in the STPU, the solution of conflict resolution constraints of Equation 9 represents the space of all relaxations, which is the same as the dynamically controllable envelope.…”