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.

翻译：针对Gamarnik与Smedira提出的问题，我们给出一个多项式时间算法以近似计算独立集多面体松弛的截断体积，改进了其拟多项式时间算法。该算法通过将体积视为图多项式在特定点的估值实现，并利用Barvinok插值方法对该估值进行近似。