Carlo Comin

Dynamic Consistency of Conditional Simple Temporal Networks via Mean Payoff Games: A Singly-Exponential Time DC-checking

Conditional Simple Temporal Network (CSTN) is a constraint-based graph-formalism for conditional temporal planning. It offers a more flexible formalism than the equivalent CSTP model of Tsamardinos, Vidal and Pollack, from which it was derived mainly as a sound formalization. Three notions of consistency arise for CSTNs and CSTPs: weak, strong, and dynamic. Dynamic consistency is the most interesting notion, but it is also the most challenging and it was conjectured to be hard to assess. Tsamardinos, Vidal and Pollack gave a doubly-exponential time algorithm for deciding whether a CSTN is dynamically-consistent and to produce, in the positive case, a dynamic execution strategy of exponential size. In the present work we offer a proof that deciding whether a CSTN is dynamically-consistent is coNP-hard and provide the first singly-exponential time algorithm for this problem, also producing a dynamic execution strategy whenever the input CSTN is dynamically-consistent. The algorithm is based on a novel connection with Mean Payoff Games, a family of two-player infinite games played on finite graphs, well known for having applications in model-checking and formal verification. The presentation of such connection is mediated by the Hyper Temporal Network model, a tractable generalization of Simple Temporal Networks whose consistency checking is equivalent to determining Mean Payoff Games. In order to analyse the algorithm we introduce a refined notion of dynamic-consistency, named ε-dynamic-consistency, and present a sharp lower bounding analysis on the critical value of the reaction time where the CSTN transits from being, to not being, dynamically-consistent. The proof technique introduced in this analysis of the reaction time is applicable more generally when dealing with linear difference constraints which include strict inequalities.

Improved Pseudo-polynomial Bound for the Value Problem and Optimal Strategy Synthesis in Mean Payoff Games

In this work we offer an

An Improved Upper Bound on Maximal Clique Listing via Rectangular Fast Matrix Multiplication

O(|V|^2 |E|\, W)

Instantaneous Reaction-Time in Dynamic-Consistency Checking of Conditional Simple Temporal Networks

O(|V|2|E|W) pseudo-polynomial time deterministic algorithm for solving the Value Problem and Optimal Strategy Synthesis in Mean Payoff Games. This improves by a factor

Sorting with Forbidden Intermediates

\log (|V|\, W)

On Restricted Disjunctive Temporal Problems: Faster Algorithms and Tractability Frontier.

log(|V|W) the best previously known pseudo-polynomial time upper bound due to Brim et al. The improvement hinges on a suitable characterization of values, and a description of optimal positional strategies, in terms of reweighted Energy Games and Small Energy-Progress Measures.