Deterministic Polynomial-Time Approximation Algorithms for Partition Functions and Graph Polynomials

In this paper we give a deterministic polynomial-time approximation algorithm for computing complex-valued evaluations of the Tutte polynomial and the independence polynomial on bounded degree graphs, as well for computing partition functions of complex-valued spin and edge-coloring models on bounded degree graphs. Our work builds on a recent line of work initiated by Barvinok [2, 3, 4, 5], which provides a new algorithmic approach besides the existing correlation decay method for these types of problems.