Better and Simpler Reducibility Bounds over the Integers

TL;DR

This paper introduces a method to replace complex integer-valued functions with simpler, smaller domain functions, enabling the transformation of weakly polynomial algorithms into strongly polynomial ones, thus improving computational efficiency.

Contribution

It presents a novel approach to reduce the domain of integer functions, facilitating the conversion of weakly polynomial algorithms into strongly polynomial algorithms.

Findings

Effective domain reduction for integer functions

Transformation of weakly polynomial algorithms into strongly polynomial algorithms

Enhanced computational efficiency in algorithm design

Abstract

We study the settings where we are given a function of n variables defined in a given box of integers. We show that in many cases we can replace the given objective function by a new function with a much smaller domain. Our approach allows us to transform a family of weakly polynomial time algorithms into strongly polynomial time algorithms.