Geometric rounding: a dependent randomized rounding scheme

  • Authors:

  • Dongdong Ge;Simai He;Yinyu Ye;Jiawei Zhang

  • Affiliations:

  • Department of Management Science, Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai, China;Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong;Department of Management Science and Engineering, Stanford University, Stanford, USA;Stern School of Business, IOMS-Operations Management, New York University, New York, USA 10012

  • Venue:
  • Journal of Combinatorial Optimization
  • Year:
  • 2011

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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.