منابع مشابه
Towards Optimal Range Medians
We consider the following problem: Given an unsorted array of n elements, and a sequence of intervals in the array, compute the median in each of the subarrays defined by the intervals. We describe a simple algorithm which needs O(n log k + k logn) time to answer k such median queries. This improves previous algorithms by a logarithmic factor and matches a comparison lower bound for k = O(n). T...
متن کاملRange Medians
We study a generalization of the classical median finding problem to batched query case: given an array of unsorted n items and k intervals in the array, the goal is to determine the median in each of the intervals in the array. We give an algorithm that uses O(n log k) comparisons and show a matching lower bound of Ω(n log k) comparisons for this problem.
متن کاملGeometric medians
We discuss several generalizations of the notion of median to points in $R^d$. They arise in Computational Geometry and in Statistics. The notions are compared with respect to some of their mathematical properties. We also consider computational aspects. The issue of computational complexity raises several intriguing questions.
متن کاملNearest-neighbors medians clustering
We propose a nonparametric cluster algorithm based on local medians. Each observation is substituted by its local median and this new observation moves toward the peaks and away from the valleys of the distribution. The process is repeated until each observation converges to a fixpoint. We obtain a partition of the sample based on the convergence points. Our algorithm determines the number of c...
متن کاملInterpolation of medians
Take n > 0 and n + 1 disjoint, bounded intervals I0, . . . , In, possible single points. In [2], motivated by applications in signal processing, it was conjectured that for any numbers a0, . . . , an, there is a unique polynomial of degree n whose median value on Ij equals aj for j = 0, . . . ,n, and this was confirmed for n = 2. We shall verify this conjecture in section 2. Indeed we prove a m...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2011
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2010.05.003