Geometric Optimization Problems Over Sliding Windows

  • Timothy M. Chan
  • Bashir S. Sadjad
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3341)


We study the problem of maintaining a (1+ε)-factor approximation of the diameter  of a stream of points under the sliding window   model. In one dimension, we give a simple algorithm that only needs to store \(O(\frac{1}{\epsilon}{\rm log}R)\) points at any time, where the parameter R denotes the “spread” of the point set. This bound is optimal and improves Feigenbaum, Kannan, and Zhang’s recent solution by two logarithmic factors. We then extend our one-dimensional algorithm to higher constant dimensions and, at the same time, correct an error in the previous solution. In high nonconstant dimensions, we also observe a constant-factor approximation algorithm that requires sublinear space. Related optimization problems, such as the width, are also considered in the two-dimensional case.


Approximation Algorithm Data Stream Computational Geometry Sliding Window Related Optimization Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Timothy M. Chan
    • 1
  • Bashir S. Sadjad
    • 1
  1. 1.School of Computer ScienceUniversity of WaterlooWaterlooCanada

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