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 t...

The Exponential-Time Hypothesis ( \mathtt {ETH} ) is a strengthening of the \mathcal {P} \ne {NP} conjecture, stating that 3\text{-}\mathtt {SAT} on n variables cannot be solved in (uniform) time 2^{\epsilon \cdot n} , for some \epsilon \gt 0 . In recent years, analogous hypotheses are “exponentially-strong” forms other classical complexity conjectures (such as {NP}\nsubseteq {BPP} or co\mathca...