Artem Nesiolovskiy | Searcharxiv

arXiv2019

Multiplication method for factoring natural numbers

We offer multiplication method for factoring big natural numbers which extends the group of the Fermat's and Lehman's factorization algorithms and has run-time complexity $O(n^{1/3})$. This paper is argued the finiteness of proposed algorithm depending on the value of the factorizable number n. We provide here comparative tests results of related algorithms on a large amount of computational checks. We describe identified advantages of the proposed algorithm over others. The possibilities of algorithm optimization for reducing the complexity of factorization are also shown here.

cs.DS↗

arXiv2012

BIN@ERN: Binary-Ternary Compressing Data Coding

This paper describes a new method of data encoding which may be used in various modern digital, computer and telecommunication systems and devices. The method permits the compression of data for storage or transmission, allowing the exact original data to be reconstructed without any loss of content. The method is characterized by the simplicity of implementation, as well as high speed and compression ratio. The method is based on a unique scheme of binary-ternary prefix-free encoding of characters of the original data. This scheme does not require the transmission of the code tables from encoder to decoder; allows for the linear presentation of the code lists; permits the usage of computable indexes of the prefix codes in a linear list for decoding; makes it possible to estimate the compression ratio prior to encoding; makes the usage of multiplication and division operations, as well as operations with the floating point unnecessary; proves to be effective for static as well as adaptive coding; applicable to character sets of any size; allows for repeated compression to improve the ratio.

cs.IT↗