Journal of Combinatorial Optimization

, Volume 22, Issue 4, pp 699–725 | Cite as

Geometric rounding: a dependent randomized rounding scheme

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


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.


Integer programming Linear programming Approximation algorithm Randomized rounding 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Management Science, Antai College of Economics and ManagementShanghai Jiao Tong UniversityShanghaiChina
  2. 2.Department of Systems Engineering and Engineering ManagementThe Chinese University of Hong KongShatinHong Kong
  3. 3.Department of Management Science and EngineeringStanford UniversityStanfordUSA
  4. 4.Stern School of Business, IOMS-Operations ManagementNew York UniversityNew YorkUSA

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