A new algorithm for solving the rSUM problem
Data Structures and Algorithms
2015-02-10 v5 Computational Complexity
Computational Geometry
Number Theory
Abstract
A determined algorithm is presented for solving the rSUM problem for any natural r with a sub-quadratic assessment of time complexity in some cases. In terms of an amount of memory used the obtained algorithm is the nlog^3(n) order. The idea of the obtained algorithm is based not considering integer numbers, but rather k (is a natural) successive bits of these numbers in the binary numeration system. It is shown that if a sum of integer numbers is equal to zero, then the sum of numbers presented by any k successive bits of these numbers must be sufficiently "close" to zero. This makes it possible to discard the numbers, which a fortiori, do not establish the solution.
Cite
@article{arxiv.1407.4640,
title = {A new algorithm for solving the rSUM problem},
author = {Valerii Sopin},
journal= {arXiv preprint arXiv:1407.4640},
year = {2015}
}