Approximating the volume of a truncated relaxation of the independence polytope

TL;DR

This paper presents a polynomial-time algorithm for approximating the volume of a truncated relaxation of the independence polytope, improving computational efficiency over previous methods by leveraging graph polynomial evaluation and Barvinok's interpolation.

Contribution

It introduces a novel polynomial-time approximation algorithm for the volume of a relaxation of the independence polytope, answering an open question and improving upon prior quasi-polynomial algorithms.

Findings

Provides a polynomial-time approximation algorithm.

Uses graph polynomial evaluation and Barvinok's interpolation method.

Achieves improved computational efficiency over previous algorithms.

Abstract

Answering a question of Gamarnik and Smedira, we give a polynomial time algorithm that approximately computes the volume of a truncation of a relaxation of the independent set polytope, improving on their quasi-polynomial time algorithm. Our algorithm is obtained by viewing the volume as an evaluation of a graph polynomial and we approximate this evaluation using Barvinok's interpolation method.