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Efficient Two-Dimensional Packing Algorithms for Mobile WiMAX

Author

Listed:
  • Andrea Lodi

    (Department of Electronics, Computer Science and Systems, University of Bologna, 40136 Bologna, Italy)

  • Silvano Martello

    (Department of Electronics, Computer Science and Systems, University of Bologna, 40136 Bologna, Italy)

  • Michele Monaci

    (Department of Information Engineering, University of Padova, 35131 Padova, Italy)

  • Claudio Cicconetti

    (Intecs S.p.A., 56121 Pisa, Italy)

  • Luciano Lenzini

    (Department of Information Engineering, University of Pisa, 56010 Pisa, Italy)

  • Enzo Mingozzi

    (Department of Information Engineering, University of Pisa, 56010 Pisa, Italy)

  • Carl Eklund

    (Nokia Siemens Networks, FI-02610 Espoo, Finland)

  • Jani Moilanen

    (Nokia Siemens Networks, FI-02610 Espoo, Finland)

Abstract

We present the result of research, developed within Nokia Siemens Networks, to solve the downlink sub-frame allocation problem in Mobile WiMAX (IEEE 802.16) technology in its full complexity, while simultaneously fulfilling real-life constraints on processing power and delay. We describe the IEEE 802.16 standard, and introduce two system models. A theoretical analysis of the two-dimensional packing problems originated by such models shows that they are both NP-hard in the strong sense. From a practical point of view, the processing budget for scheduling in the base station was estimated to be 1 ms on a state-of-the-art PC. Thus, we introduce two highly efficient heuristics that were developed to handle the system practically. A thorough computational analysis of their optimization characteristics and a system-level evaluation in realistic scenarios proved that the algorithms offer significant capacity gain in Mobile WiMAX systems that translate to increased operator revenues. This paper was accepted by Dimitris Bertsimas, optimization.

Suggested Citation

  • Andrea Lodi & Silvano Martello & Michele Monaci & Claudio Cicconetti & Luciano Lenzini & Enzo Mingozzi & Carl Eklund & Jani Moilanen, 2011. "Efficient Two-Dimensional Packing Algorithms for Mobile WiMAX," Management Science, INFORMS, vol. 57(12), pages 2130-2144, December.
    • Handle: RePEc:inm:ormnsc:v:57:y:2011:i:12:p:2130-2144
    DOI: 10.1287/mnsc.1110.1416
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    References listed on IDEAS

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    1. Lodi, Andrea & Martello, Silvano & Monaci, Michele, 2002. "Two-dimensional packing problems: A survey," European Journal of Operational Research, Elsevier, vol. 141(2), pages 241-252, September.
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    Cited by:

    1. Malaguti, Enrico & Monaci, Michele & Paronuzzi, Paolo & Pferschy, Ulrich, 2019. "Integer optimization with penalized fractional values: The Knapsack case," European Journal of Operational Research, Elsevier, vol. 273(3), pages 874-888.
    2. Iori, Manuel & de Lima, Vinícius L. & Martello, Silvano & Miyazawa, Flávio K. & Monaci, Michele, 2021. "Exact solution techniques for two-dimensional cutting and packing," European Journal of Operational Research, Elsevier, vol. 289(2), pages 399-415.
    3. Arbib, Claudio & Marinelli, Fabrizio & Pizzuti, Andrea, 2021. "Number of bins and maximum lateness minimization in two-dimensional bin packing," European Journal of Operational Research, Elsevier, vol. 291(1), pages 101-113.
    4. Sergey Kovalev, 2022. "Approximation issues of fractional knapsack with penalties: a note," 4OR, Springer, vol. 20(2), pages 209-216, June.
    5. Fabio Furini & Enrico Malaguti & Dimitri Thomopulos, 2016. "Modeling Two-Dimensional Guillotine Cutting Problems via Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 736-751, November.
    6. Michele Monaci & André Gustavo Santos, 2018. "Minimum tiling of a rectangle by squares," Annals of Operations Research, Springer, vol. 271(2), pages 831-851, December.

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