Faster exponential-time algorithms for approximately counting independent sets

Counting the independent sets of a graph is classical #P-complete problem, even in bipartite case. We give an exponential-time approximation scheme for this problem which faster than best known algorithm exact problem. The running time our on general graphs with error tolerance ε at most O(20.2680n) times polynomial 1/ε. On graphs, exponential term improved to O(20.2372n). Our methods combine techniques from algorithms approximate counting. Along way we generalise (to multivariate case) FPTAS Sinclair, Srivastava, Štefankovič and Yin approximating hard-core partition function bounded connective constant. Also, obtain counting no vertices degree least 6 whose neighbours' degrees sum 27 or more. By result Sly, there that applies all maximum unless P=NP.