Energy-Efficient Fast Delivery by Mobile Agents

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10472)

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].

Notes

Acknowledgments

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

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Computer ScienceETH ZürichZürichSwitzerland

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