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Charlemagne's Challenge: The Periodic Latency Problem

Author

Listed:
  • Sofie Coene

    (Operations Research Group, Katholieke Universiteit Leuven, B-3000 Leuven, Belgium)

  • Frits C. R. Spieksma

    (Operations Research Group, Katholieke Universiteit Leuven, B-3000 Leuven, Belgium)

  • Gerhard J. Woeginger

    (Department of Mathematics, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands)

Abstract

Latency problems are characterized by their focus on minimizing the waiting time for all clients. We study periodic latency problems, a nontrivial extension of standard latency problems. In a periodic latency problem each client has to be visited regularly: there is a server traveling at unit speed, and there is a set of n clients with given positions. The server must visit the clients over and over again, subject to the constraint that successive visits to client i are at most q i time units away from each other.We investigate two main problems. In problem PLPP the goal is to find a repeatable route for the server visiting as many clients as possible without violating their q i s. In problem PLP the goal is to minimize the number of servers needed to serve all clients. Depending on the topology of the underlying network, we derive polynomial-time algorithms or hardness results for these two problems. Our results draw sharp separation lines between easy and hard cases.

Suggested Citation

  • Sofie Coene & Frits C. R. Spieksma & Gerhard J. Woeginger, 2011. "Charlemagne's Challenge: The Periodic Latency Problem," Operations Research, INFORMS, vol. 59(3), pages 674-683, June.
    • Handle: RePEc:inm:oropre:v:59:y:2011:i:3:p:674-683
    DOI: 10.1287/opre.1110.0919
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    References listed on IDEAS

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