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Geometric rounding: a dependent randomized rounding scheme

Author

Listed:
  • Dongdong Ge

    (Shanghai Jiao Tong University)

  • Simai He

    (The Chinese University of Hong Kong)

  • Yinyu Ye

    (Stanford University)

  • Jiawei Zhang

    (New York University)

Abstract

We develop a new dependent randomized rounding method for approximation of a number of optimization problems with integral assignment constraints. The core of the method is a simple, intuitive, and computationally efficient geometric rounding that simultaneously rounds multiple points in a multi-dimensional simplex to its vertices. Using this method we obtain in a systematic way known as well as new results for the hub location, metric labeling, winner determination and consistent labeling problems. A comprehensive comparison to the dependent randomized rounding method developed by Kleinberg and Tardos (J. ACM 49(5):616–639, 2002) and its variants is also conducted. Overall, our geometric rounding provides a simple and effective alternative for rounding various integer optimization problems.

Suggested Citation

  • Dongdong Ge & Simai He & Yinyu Ye & Jiawei Zhang, 2011. "Geometric rounding: a dependent randomized rounding scheme," Journal of Combinatorial Optimization, Springer, vol. 22(4), pages 699-725, November.
    • Handle: RePEc:spr:jcomop:v:22:y:2011:i:4:d:10.1007_s10878-010-9320-z
    DOI: 10.1007/s10878-010-9320-z
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    References listed on IDEAS

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    1. James F. Campbell, 1996. "Hub Location and the p -Hub Median Problem," Operations Research, INFORMS, vol. 44(6), pages 923-935, December.
    2. Morton O'Kelly & Darko Skorin-Kapov & Jadranka Skorin-Kapov, 1995. "Lower Bounds for the Hub Location Problem," Management Science, INFORMS, vol. 41(4), pages 713-721, April.
    3. A.A. Ageev & M.I. Sviridenko, 2004. "Pipage Rounding: A New Method of Constructing Algorithms with Proven Performance Guarantee," Journal of Combinatorial Optimization, Springer, vol. 8(3), pages 307-328, September.
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