Approximate counting using Taylor's theorem: a survey
Abstract
In this article we consider certain well-known polynomials associated with graphs including the independence polynomial and the chromatic polynomial. These polynomials count certain objects in graphs: independent sets in the case of the independence polynomial and proper colourings in the case of the chromatic polynomial. They also have interpretations as partition functions in statistical physics. The algorithmic problem of (approximately) computing these types of polynomials has been studied for close to 50 years, especially using Markov chain techniques. Around eight years ago, Barvinok devised a new algorithmic approach based on Taylor's theorem for computing the permanent of certain matrices, and the approach has been applied to various graph polynomials since then. This article is intended as a gentle introduction to the approach as well as a partial survey of associated techniques and results.
Cite
@article{arxiv.2212.08143,
title = {Approximate counting using Taylor's theorem: a survey},
author = {Viresh Patel and Guus Regts},
journal= {arXiv preprint arXiv:2212.08143},
year = {2022}
}
Comments
28 pages. Published in the October issue of the Bulletin of the EATC. This is a survey article and does not contain any new results