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Nearly optimal bounds for distributed wireless scheduling in the SINR model

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Abstract

We study the wireless scheduling problem in the SINR model. More specifically, given a set of \(n\) links, each a sender–receiver pair, we wish to partition (or schedule) the links into the minimum number of slots, each satisfying interference constraints allowing simultaneous transmission. In the basic problem, all senders transmit with the same uniform power. We analyze a randomized distributed scheduling algorithm proposed by Kesselheim and Vöcking, and show that it achieves \(O(\log n)\)-approximation, an improvement of a logarithmic factor. This matches the best ratio known for centralized algorithms and holds in arbitrary metric space and for every length-monotone and sublinear power assignment. We also show that every distributed algorithm uses \(\varOmega (\log n)\) slots to schedule certain instances that require only two slots, which implies that the best possible absolute performance guarantee is logarithmic.

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Notes

  1. 1.

    For a technical reason we use a different constant here than for feasibility; the signal-strengthening result of [17] implies that this only affects constants in the approximation factors.

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Acknowledgments

We thank Marijke Bodlaender for helpful discussions leading to the derivation of Lemma 7.

Author information

Correspondence to Magnús M. Halldórsson.

Additional information

Supported by Grants 90032021 and 120032011 from the Icelandic Research Fund. Preliminary version appeared in ICALP 2011.

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Halldórsson, M.M., Mitra, P. Nearly optimal bounds for distributed wireless scheduling in the SINR model. Distrib. Comput. 29, 77–88 (2016). https://doi.org/10.1007/s00446-014-0222-7

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Keywords

  • Wireless
  • Scheduling
  • SINR model