Streaming Algorithms for Extent Problems in High Dimensions
Algorithmica(2013)
摘要
We present (single-pass) streaming algorithms for maintaining extent measures of a stream S of n points in ℝ ^d . We focus on designing streaming algorithms whose working space is polynomial in d (poly( d )) and sub-linear in n . For the problems of computing diameter, width and minimum enclosing ball of S , we obtain lower bounds on the worst-case approximation ratio of any streaming algorithm that uses poly( d ) space. On the positive side, we introduce the notion of blurred ball cover and use it for answering approximate farthest-point queries and maintaining approximate minimum enclosing ball and diameter of S . We describe a streaming algorithm for maintaining a blurred ball cover whose working space is linear in d and independent of n .
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关键词
Streaming algorithms,Computational geometry,Extent problems,Minimum enclosing ball,Diameter
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