Fractal Analysis of the Subset-Sum Problem

Ruben Horn, Daan van den Berg, Daan van den Berg, Pieter Adriaans

2024

Abstract

It is known that the hardness of the (two-way) number partitioning problem (NPP) variant of the subset-sum problem (SSP) depends on the number and distribution of bits in the set of numbers, but beyond this, it is relatively unexplained for the SSP itself. Thus, we look at the solution space of various problem instances of the SSP using fractal analysis. Two methods to determine the dimension are used. Plotting the fractal dimension over the range and distributions of informational bits, we find that it is correlated with this linear model and also moderately correlated to the hardness of the NPP. This suggests that fractal analysis might be a useful tool in understanding the complexity of combinatorial problems and, we believe, may help further understand the hardness in NP. Finally, we introduce a thought experiment derived from the famous Hilbert’s hotel, which we call Hilbert’s hotel with elevators, to intuitively illustrate how the complexity of the solutions space and the computational hardness may relate across combinatorial problems.

Paper Citation

in Harvard Style

Horn R., van den Berg D. and Adriaans P. (2024). Fractal Analysis of the Subset-Sum Problem. In Proceedings of the 16th International Joint Conference on Computational Intelligence - Volume 1: ECTA; ISBN 978-989-758-721-4, SciTePress, pages 261-268. DOI: 10.5220/0012990400003837

in Bibtex Style

@conference{ecta24,
author={Ruben Horn and Daan van den Berg and Pieter Adriaans},
title={Fractal Analysis of the Subset-Sum Problem},
booktitle={Proceedings of the 16th International Joint Conference on Computational Intelligence - Volume 1: ECTA},
year={2024},
pages={261-268},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0012990400003837},
isbn={978-989-758-721-4},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 16th International Joint Conference on Computational Intelligence - Volume 1: ECTA
TI - Fractal Analysis of the Subset-Sum Problem
SN - 978-989-758-721-4
AU - Horn R.
AU - van den Berg D.
AU - Adriaans P.
PY - 2024
SP - 261
EP - 268
DO - 10.5220/0012990400003837
PB - SciTePress