Approximating Majority Depth
نویسندگان
چکیده
We consider the problem of approximating the majority depth (Liu and Singh, 1993) of a point q with respect to an n-point set, S, by random sampling. At the heart of this problem is a data structures question: How can we preprocess a set of n lines so that we can quickly test whether a randomly selected vertex in the arrangement of these lines is above or below the median level. We describe a Monte-Carlo data structure for this problem that can be constructed in O(n logn) time, can answer queries in O((log n)) expected time, and answers correctly with high probability.
منابع مشابه
Bounds on the Size of Small Depth Circuits for Approximating Majority
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