A Probabilistic Attack on NP-complete Problems
Computational Complexity
2012-08-06 v3 Artificial Intelligence
Discrete Mathematics
Data Structures and Algorithms
Abstract
Using the probability theory-based approach, this paper reveals the equivalence of an arbitrary NP-complete problem to a problem of checking whether a level set of a specifically constructed harmonic cost function (with all diagonal entries of its Hessian matrix equal to zero) intersects with a unit hypercube in many-dimensional Euclidean space. This connection suggests the possibility that methods of continuous mathematics can provide crucial insights into the most intriguing open questions in modern complexity theory.
Cite
@article{arxiv.1107.0098,
title = {A Probabilistic Attack on NP-complete Problems},
author = {Alexander Y. Davydov},
journal= {arXiv preprint arXiv:1107.0098},
year = {2012}
}
Comments
16 pages, 8 figures, 2 tables