Abstract. We study the variety of subtrees lying on the fringe of recursive trees and binary search trees by analyzing the distributional behavior of Xn,k, which counts the number of subtrees of size k in a random tree of size n, with k = k(n) dependent on n. Using analytic methods we can characterize for both tree families the phase change behavior of Xn,k as follows. In the subcritical case, ...

Color quantization is a useful method for obtaining high-quality compressed images for storage and subsequent distribution via the World Wide Web. The first step of most color quantization techniques is to create a histogram of the colors in the truecolor image. The dramatic differences in time and space efficiency of various data structures used to represent truecolor image histograms are visu...

which simply counts the number of coordinates where the points differ. Consider now the following simple hash family: H = {hk | hk(~x) = k bit of ~x} Such a hash function maps each item to one of two buckets. Let Zij denote the random variable that is d if items xi and xj map to different buckets and 0 otherwise, where the randomness is over the hash function chosen from H. Then it is easy to c...

Randomized algorithms and data structures are often analyzed under the assumption of access to a perfect source of randomness. The most fundamental metric used to measure how “random” a hash function or a random number generator is, is its independence: a sequence of random variables is said to be k-independent if every variable is uniform and every size k subset is independent. In this paper w...

The framework of this paper is supervised learning using classification trees. Two types of variables play a role in the definition of the classification rule, namely a response variable and a set of predictors. The tree classifier is built up by a recursive partitioning of the prediction space such to provide internally homogeneous groups of objects with respect to the response classes. In the...

The PEP-II storage rings at SLAC each have 3492 ’buckets’ into which electrons and positrons can be injected into the highand low-energy rings. Equipment to measure the currents of all the individual buckets was originally provided by the Lawrence Berkeley Laboratory and is implemented in VXI-based hardware. Data from this equipment as well as high precision direct current measurement provide t...