# Fastest Known Algorithm to Count Acyclic Orientations in a Graph

Given an undirected graph $$G$$, an acyclic orientation of $$G$$ is choice of orientation for each edge of $$G$$ (turning each edge into an arc) such that the resulting directed graph has no directed cycles.

Question: Given an undirected graph $$G$$ on $$n$$ nodes, what is the fastest known algorithm for counting the number of acyclic orientations of $$G$$?

I believe this problem can be solved in $$2^n\text{poly}(n)$$ time using existing inclusion-exclusion or fast subset convolution ideas (although I haven't verified the details of such an algorithm), but I'm curious to know if there an algorithm solving this problem in $$c^n$$ time for some constant $$c < 2$$.