Paper 2022/1113
A new algorithm for solving the rSUM problem
, Independent scientistAbstract
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.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Preprint.
- Keywords
- 3SUM (kSUM) problem computational complexity computational geometry knapsack problem structure of sumsets
- Contact author(s)
- vVs @ myself com
- History
- 2022-08-29: approved
- 2022-08-28: received
- See all versions
- Short URL
- https://ia.cr/2022/1113
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2022/1113,
author = {Valerii Sopin},
title = {A new algorithm for solving the {rSUM} problem},
howpublished = {Cryptology {ePrint} Archive, Paper 2022/1113},
year = {2022},
url = {https://eprint.iacr.org/2022/1113}
}
