Universally Hard Hamiltonian Cycle Problem Instances

Joeri Sleegers, Sarah Thomson, Daan van Den Berg

2022

Abstract

In 2021, evolutionary algorithms found the hardest-known yes and no instances for the Hamiltonian cycle problem. These instances, which show regularity patterns, require a very high number of recursions for the best exact backtracking algorithm (Vandegriend-Culberson), but don’t show up in large randomized instance ensembles. In this paper, we will demonstrate that these evolutionarily found instances of the Hamiltonian cycle problem are hard for all major backtracking algorithms, not just the Vandegriend-Culberson. We compare performance of these six algorithms on an ensemble of 91,000 randomized instances plus the evolutionarily found instances. These results present a first glance at universal hardness for this NP-complete problem. Algorithms, source code, and input data are all publicly supplied to the community.

Paper Citation

in Harvard Style

Sleegers J., Thomson S. and van Den Berg D. (2022). Universally Hard Hamiltonian Cycle Problem Instances. In Proceedings of the 14th International Joint Conference on Computational Intelligence (IJCCI 2022) - Volume 1: ECTA; ISBN 978-989-758-611-8, SciTePress, pages 105-111. DOI: 10.5220/0011531900003332

in Bibtex Style

@conference{ecta22,
author={Joeri Sleegers and Sarah Thomson and Daan van Den Berg},
title={Universally Hard Hamiltonian Cycle Problem Instances},
booktitle={Proceedings of the 14th International Joint Conference on Computational Intelligence (IJCCI 2022) - Volume 1: ECTA},
year={2022},
pages={105-111},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0011531900003332},
isbn={978-989-758-611-8},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 14th International Joint Conference on Computational Intelligence (IJCCI 2022) - Volume 1: ECTA
TI - Universally Hard Hamiltonian Cycle Problem Instances
SN - 978-989-758-611-8
AU - Sleegers J.
AU - Thomson S.
AU - van Den Berg D.
PY - 2022
SP - 105
EP - 111
DO - 10.5220/0011531900003332
PB - SciTePress