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• W2057435778 abstract "Many divide-and-conquer based geometric algorithms and order-statistics problems ask for a point that lies the middle of a given point set. We study several fun- damental problems of this type for moving points in one and two dimensions. In particular, we show how to kinetically maintain the median of a set of n points moving on the real line, and a center point of a set of n points moving in the plane, that is, a point such that any line through it has at most 2n/3 on either side of it. Since the maintenance of exact medians and center points can be quite expensive, we also show how to maintain -approximate medians and center points and argue that the latter can be made to be much more stable under motion. These results are based on a new algorithm to maintain an -approximation of a range space under insertions and deletions, which is of independent interest. All our approximation algorithms run in near-linear time." @default.
• W2057435778 created "2016-06-24" @default.
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• W2057435778 date "2005-01-01" @default.
• W2057435778 modified "2023-09-25" @default.
• W2057435778 title "Staying in the middle : exact and approximate medians in R1 and R2 for moving points" @default.
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