Hyper temporal networks

Comin, Carlo; Posenato, Roberto; Rizzi, Roméo

doi:10.1007/s10601-016-9243-0

Cited by 8 publications

(21 citation statements)

References 13 publications

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“…The tightest worst-case time complexity for solving HyTN-Consistency is expressed by the following theorem, which was proven by resorting to the Value Iteration Algorithm for MPGs [3]. The approach was shown to be robust by experimental evaluations in [2], [8], where HyTNs of size ∼ 10 6 were solved within ∼ 5 sec.…”

Section: Definition 11 (Hypergraph)mentioning

confidence: 99%

“…The converse is not true because feasible schedules for a HyTN do not need to form a convex polytope [7], [8] whereas, in general, the feasible schedules of an STN are the solutions of a linear system and, therefore, they form a convex polytope.…”

Section: Definition 11 (Hypergraph)mentioning

confidence: 99%

“…The computational equivalence between checking the consistency of HyTNs and determining the winning regions of MPGs was pointed out in [7], [8]. The tightest worst-case time complexity for solving HyTN-Consistency is expressed by the following theorem, which was proven by resorting to the Value Iteration Algorithm for MPGs [3].…”

Section: Definition 11 (Hypergraph)mentioning

confidence: 99%

“…Recently, STNs have been generalized into Hyper Temporal Networks (HyTNs) [7], [8] by considering weighted directed hypergraphs, where each hyperarc models a disjunctive temporal constraint called hyper-constraint. The computational equivalence between checking the consistency of HyTNs and determining winning regions in Mean Payoff Games (MPGs) [3], [10], [17] was pointed out as well in [7], [8], where the approach was shown to be robust thanks to extensive experimental evaluations [2], [7], [8]. Mean Payoff Games are a family of two-player infinite games played on finite graphs, well known for having theoretical interest in computational complexity, being it one of the few (natural) problems lying in NP ∩ coNP, as well as various applications in model-checking and formal verification [11].…”

Section: Introductionmentioning

confidence: 99%

“…The difference, however, is that we propose to map CSTNs on HyTNs/MPGs rather than on DTPs. This makes a relevant difference since the consistency check for HyTNs can be reduced to MPGs determination [7], [8], which is amenable to practical and effective pseudo-polynomial time algorithms (indeed, in several cases the resolution methods for determining MPGs exhibit even a strongly-polynomial time behaviour [1], [2], [4], [8]). To summarize, we obtain an improved upper bound on the theoretical time complexity of the DC-checking for CSTNs (i.e., from 2-EXP to NE ∩ coNE) together with a faster DC-checking procedure, which can be used on CSTNs with a larger number of propositional variables and event nodes.…”

Section: Introductionmentioning

confidence: 99%

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

Comin

Rizzi

2015

2015 22nd International Symposium on Temporal Representation and Reasoning (TIME)

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Abstract-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 dynamicallyconsistent 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 dynamicallyconsistent 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 analyze the algorithm we introduce a refined notion of dynamic-consistency, named -dynamic-consistency, and present a sharp lower bounding analysis on the critical value of the reaction timeε where the CSTN transits from being, to not being, dynamically-consistent. The proof technique introduced in this analysis ofε is applicable more generally when dealing with linear difference constraints which include strict inequalities.

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Section: Definition 11 (Hypergraph)mentioning

confidence: 99%

Section: Definition 11 (Hypergraph)mentioning

confidence: 99%

Section: Definition 11 (Hypergraph)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Comin

Rizzi

2015

2015 22nd International Symposium on Temporal Representation and Reasoning (TIME)

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Solving Mean-Payoff Games via Quasi Dominions

Benerecetti

Dell’Erba

Mogavero

2020

Lecture Notes in Computer Science

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We propose a novel algorithm for the solution of mean-payoff games that merges together two seemingly unrelated concepts introduced in the context of parity games, small progress measures and quasi dominions. We show that the integration of the two notions can be highly beneficial and significantly speeds up convergence to the problem solution. Experiments show that the resulting algorithm performs orders of magnitude better than the asymptotically-best solution algorithm currently known, without sacrificing on the worst-case complexity.A two-player turn-based arena is a tuple A = Ps ⊕ , Ps ⊟ , Mv , with Ps ⊕ ∩ Ps ⊟ = ∅ and Ps Ps ⊕ ∪ Ps ⊟ , such that Ps, Mv is a finite directed graph without sinks. Ps ⊕ (resp., Ps ⊟ ) is the set of 1. The experiments were carried out on a 64-bit 3.9GHz quad-core machine, with INTEL i5-6600K processor and 8GB of RAM, running UBUNTU 18.04.

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