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Energy-Efficient Fast Delivery by Mobile Agents

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Book cover Fundamentals of Computation Theory (FCT 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10472))

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Abstract

We consider the problem of collaboratively delivering a package from a specified source node s to a designated target node t in an undirected graph \(G=(V,E)\), using k mobile agents. Each agent i starts at time 0 at a node \(p_i\) and can move along edges subject to two parameters: Its weight \(w_i\), which denotes the rate of energy consumption while travelling, and its velocity \(v_i\), which defines the speed with which agent i can travel.

We are interested in operating the agents such that we minimize the total energy consumption \(\mathcal {E}\) and the delivery time \(\mathcal {T}\) (time when the package arrives at t). Specifically, we are after a schedule of the agents that lexicographically minimizes the tuple \((\mathcal {E}, \mathcal {T})\). We show that this problem can be solved in polynomial time \(\mathcal {O}(k|V|^2 + \mathrm{APSP})\), where \(\mathcal {O}(\mathrm{APSP})\) denotes the running time of an all-pair shortest-paths algorithm. This completes previous research which shows that minimizing only \(\mathcal {E}\) or only \(\mathcal {T}\) is polynomial-time solvable [6, 7], while minimizing a convex combination of \(\mathcal {E}\) and \(\mathcal {T}\), or lexicographically minimizing the tuple \((\mathcal {T},\mathcal {E})\) are both \(\mathrm {NP}\)-hard [7].

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Notes

  1. 1.

    Formally, we have \(\bigcup _c W_c = [k]\) and \(\sum _c x_c = k\) such that \(\forall c, \forall i,j \in W_c:w_i = w_j\) and \(\forall c_1 < c_2, \forall i \in W_{c_1}, \forall j \in W_{c_2}:w_i > w_j\).

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Acknowledgments

This work was partially supported by the SNF (project 200021L_156620, Algorithm Design for Microrobots with Energy Constraints).

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Authors and Affiliations

  1. Department of Computer Science, ETH Zürich, Zürich, Switzerland

    Andreas Bärtschi & Thomas Tschager

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  1. Andreas Bärtschi
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  2. Thomas Tschager
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Correspondence to Andreas Bärtschi .

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Editors and Affiliations

  1. CNRS, University of Bordeaux, Talence cedex, France

    Ralf Klasing

  2. LaBRI, University of Bordeaux, Talence cedex, France

    Marc Zeitoun

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Bärtschi, A., Tschager, T. (2017). Energy-Efficient Fast Delivery by Mobile Agents. In: Klasing, R., Zeitoun, M. (eds) Fundamentals of Computation Theory. FCT 2017. Lecture Notes in Computer Science(), vol 10472. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55751-8_8

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  • DOI: https://doi.org/10.1007/978-3-662-55751-8_8

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