منابع مشابه
Approximating Majority Depth
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 M...
متن کاملBounds on the Size of Small Depth Circuits for Approximating Majority
In this paper, we show that for every constant 0 < ǫ < 1/2 and for every constant d ≥ 2, the minimum size of a depth d Boolean circuit that ǫ-approximates Majority function on n variables is exp(Θ(n)). The lower bound for every d ≥ 2 and the upper bound for d = 2 have been previously shown by O’Donnell and Wimmer [ICALP’07], and the contribution of this paper is to give a matching upper bound f...
متن کاملApproximating the Simplicial Depth
Let P be a set of n points in d-dimensions. The simplicial depth, σP (q) of a point q is the number of d-simplices with vertices in P that contain q in their convex hulls. The simplicial depth is a notion of data depth with many applications in robust statistics and computational geometry. Computing the simplicial depth of a point is known to be a challenging problem. The trivial solution requi...
متن کاملAlgorithms for Bivariate Majority Depth
The majority depth of a point with respect to a point set is the number of major sides it is in. An algorithm for majority depth in R is given in this paper, and it is the first algorithm to compute the majority depth. This algorithm runs in O((n+m) log n) time with Brodal and Jacob’s data structure, and in O ( (n + m) log n log log n ) time in the word RAM model.
متن کاملThreshold Circuits of Small Majority-Depth
Constant-depth polynomial-size threshold circuits are usually classi ed according to their total depth. For example, the best known threshold circuits for iterated multiplication and division have depth four and three, respectively. In this paper, the complexity of threshold circuits is investigated from a di erent point of view: explicit AND, OR gates are allowed in the circuits, and a thresho...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2015
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2013.11.005