Computing a Knot Invariant as a Constraint Satisfaction Problem
Disordered Systems and Neural Networks
2015-06-03 v1 Statistical Mechanics
Computational Complexity
Abstract
We point out the connection between mathematical knot theory and spin glass/search problem. In particular, we present a statistical mechanical formulation of the problem of computing a knot invariant; p-colorability problem, which provides an algorithm to find the solution. The method also allows one to get some deeper insight into the structural complexity of knots, which is expected to be related with the landscape structure of constraint satisfaction problem.
Cite
@article{arxiv.1111.1060,
title = {Computing a Knot Invariant as a Constraint Satisfaction Problem},
author = {Chihiro H. Nakajima and Takahiro Sakaue},
journal= {arXiv preprint arXiv:1111.1060},
year = {2015}
}
Comments
6 pages, 3 figures, submitted to short note in Journal of Physical Society of Japan