Simple deterministic O(n log n) algorithm finding a solution of Erd\H{o}s-Ginzburg-Ziv theorem

TL;DR

This paper introduces the first deterministic algorithm with O(n log n) complexity for finding a subsequence satisfying the Erdős-Ginzburg-Ziv theorem, improving computational efficiency in additive number theory.

Contribution

The paper presents the first deterministic O(n log n) algorithm to find the required subsequence in the Erdős-Ginzburg-Ziv theorem, advancing algorithmic solutions in additive number theory.

Findings

Developed a deterministic O(n log n) algorithm

First known efficient solution for Erdős-Ginzburg-Ziv problem

Algorithm runs in optimal asymptotic time

Abstract

Erd\H{o}s-Ginzburg-Ziv theorem is a famous theorem in additive number theory, which states any sequence of $2n-1$ integers contains a subsequence of $n$ elements, with their sum being a multiple of $n$. In this article, we provide an algorithm finding a solution of Erd\H{o}s-Ginzburg-Ziv theorem in $\mathcal{O}(n \log n)$ time. This is the first known deterministic $\mathcal{O}(n \log n)$ time algorithm finding a solution of Erd\H{o}s-Ginzburg-Ziv theorem.