In this paper we provide a deterministic fully polynomial time approximation scheme (FPTAS) for counting two-rowed contingency tables that is faster than any either deterministic or randomized approximation scheme for this problem known to date. Our FPTAS is derived via a somewhat sophisticated usage of the method of K-approximation sets and functions introduced by Halman et al. [Math. Oper. Res. 34, (2009), pp. 674--685].
Hebrew University of Jerusalem