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Journal of Scheduling

, Volume 15, Issue 4, pp 473–486 | Cite as

Routing equal-size messages on a slotted ring

  • Dariusz DereniowskiEmail author
  • Wiesław Kubiak
Article
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Abstract

We deal with the problem of routing messages on a slotted ring network in this paper. We study the computational complexity and algorithms for this routing by means of the results known in the literature for the multi-slot just-in-time scheduling problem. We consider two criteria for the routing problem: makespan, or minimum routing time, and diagonal makespan. A diagonal is simply a schedule of ring links i=0,…,q−1 in q consecutive time slots, respectively. The number of diagonals between the earliest and the latest diagonals with non-empty packets is referred to as the diagonal makespan. For the former, we show that the optimal routing of messages of size k, is NP-hard in the strong sense, while an optimal routing when k=q can be computed in O(n 2log2 n) time. We also give an O(nlogn)-time constant factor approximation algorithm for unit size messages. For the latter, we prove that the optimal routing of messages of size k, where k divides the size of the ring q, is NP-hard in the strong sense even for any fixed k≥1, while an optimal routing when k=q can be computed in O(nlogn) time. We also give an O(nlogn)-time approximation algorithm with an absolute error 2qk.

Keywords

Just-in-time scheduling Multi-slot scheduling Optical network Routing Slotted ring 

Notes

Acknowledgements

This research has been supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) Grant OPG0105675. Moreover, Dariusz Dereniowski has been supported by the Foundation for Polish Science (FNP) and by the Polish Ministry of Science and Higher Education (MNiSW) grant N N516 196437.

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Algorithms and System ModelingGdańsk University of TechnologyGdańskPoland
  2. 2.Faculty of Business AdministrationMemorial UniversitySt. John’sCanada

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