On the computational complexity of MSTD sets

TL;DR

This paper presents an algorithm to verify MSTD sets, analyzes its computational complexity, and provides numerical results for large sets up to size 160, advancing understanding of sum dominated sets.

Contribution

It introduces a general algorithm for verifying MSTD sets and estimates its computational complexity, offering new tools for studying sum dominated sets.

Findings

Algorithm for verifying MSTD sets outlined

Computational complexity estimates provided

Numerical results for sets up to size 160

Abstract

We outline a general algorithm for verifying whether a subset of the integers is a more sum than differences (MSTD) set, also known as sum dominated sets, and give estimates on its computational complexity. We conclude with some numerical results on large MSTD sets and MSTD subsets of $[1,N]\cap \mathbb Z$ for $N$ up to 160.