Five Balltree Construction Algorithms
Balltrees are simple geometric data structures with a wide range of practical applica­ tions to geometric ·learning tasks. In this report we compare 5 different algorithms for . constructing ball trees from data. We study the trade-off between construction time and the quality of the constructed tree. Two of the algorithms are on-line, two construct the structures from the data set in a top down fashion, and one uses a bottom up approach. We empirically study the algorithms on random data drawn from eight different probability distributions representing smooth, clustered, and curve distributed data in different ambient space dimen­ sions. We find that the bottom up approach usually produces the best trees but has the longest construction time. The other approaches have uses in specific circumstances. 1. IntemauonaI.Computer Science Institute, Berkeley, CA.
In this paper, I will describe and demonstrate a new method to prove Goldbach’s Conjecture. The idea behind my method is to organize all natural numbers in a binary tree, and to find the connections between the even numbers and the prime numbers by using the characteristics of the tree structure.