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ISAAC
2004
Springer

Geometric Optimization Problems Over Sliding Windows

9 years 9 months ago
Geometric Optimization Problems Over Sliding Windows
Abstract. We study the problem of maintaining a (1+ )-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(1 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.
Timothy M. Chan, Bashir S. Sadjad
Added 02 Jul 2010
Updated 02 Jul 2010
Type Conference
Year 2004
Where ISAAC
Authors Timothy M. Chan, Bashir S. Sadjad
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