From Maximum Cut to Maximum Independent Set
Abstract
The Maximum Cut (Max-Cut) problem could be naturally expressed either in a Quadratic Unconstrained Binary Optimization (QUBO) formulation, or as an Ising model. It has long been known that the Maximum Independent Set (MIS) problem could also be related to a specific Ising model. Therefore, it would be natural to attack MIS with various Max-Cut/Ising solvers. It turns out that this strategy greatly improves the approximation for the independence number of random Erd\H{o}s-R\'{e}nyi graphs. It also exhibits perfect performance on a benchmark arising from coding theory. These results pave the way for further development of approximate quantum algorithms on MIS, and specifically on the corresponding coding problems.
Cite
@article{arxiv.2408.06758,
title = {From Maximum Cut to Maximum Independent Set},
author = {Chuixiong Wu and Jianan Wang and Fen Zuo},
journal= {arXiv preprint arXiv:2408.06758},
year = {2024}
}
Comments
Independence number of 1dc.2048 updated, new results for 1dc.4096 included, references added; 22 pages, 5 figures