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Hyper temporal networks

A tractable generalization of simple temporal networks and its relation to mean payoff games

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Abstract

Simple Temporal Networks (STNs) provide a powerful and general tool for representing conjunctions of maximum delay constraints over ordered pairs of temporal variables. In this paper we introduce Hyper Temporal Networks (HyTNs), a strict generalization of STNs, to overcome the limitation of considering only conjunctions of constraints but maintaining a practical efficiency in the consistency check of the instances. In a Hyper Temporal Network a single temporal hyperarc constraint may be defined as a set of two or more maximum delay constraints which is satisfied when at least one of these delay constraints is satisfied. HyTNs are meant as a light generalization of STNs offering an interesting compromise. On one side, there exist practical pseudo-polynomial time algorithms for checking consistency and computing feasible schedules for HyTNs. On the other side, HyTNs offer a more powerful model accommodating natural constraints that cannot be expressed by STNs like “Trigger off exactly δ min before (after) the occurrence of the first (last) event in a set.”, which are used to represent synchronization events in some process aware information systems/workflow models proposed in the literature.

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Notes

  1. Distance graph is also called constraint graph by other authors [17]. Moreover, Bellman [3] was the first to describe the relation between shortest paths and difference constraints in a constraint graph.

  2. A strong and basic-form of reduction introduced by Papadimitriou in [38].

  3. A restricted kind of Karp reduction introduced in [24].

  4. We considered not consistent HyTNs because they practically required more time to be solved.

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Acknowledgments

Supported by Department of Computer Science, University of Verona under PhD grant “Computational Mathematics and Biology” on a co-tutelle agreement with Université Paris-Est in Marne-la-Vallée

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Authors and Affiliations

  1. Department of Mathematics, University of Trento, Trento, Italy

    Carlo Comin

  2. LIGM, Université Paris-Est in Marne-la-Vallée, Paris, France

    Carlo Comin

  3. Department of Computer Science, University of Verona, Verona, Italy

    Roberto Posenato & Romeo Rizzi

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Correspondence to Roberto Posenato.

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Comin, C., Posenato, R. & Rizzi, R. Hyper temporal networks. Constraints 22, 152–190 (2017). https://doi.org/10.1007/s10601-016-9243-0

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