  To find the number of assignments of zeros and ones satisfying a specific
Knapsack Problem is $\#P$ hard, so only approximations are envisageable. A
Markov chain allowing uniform sampling of all possible solutions is given by
Luby, Randall and Sinclair. In 2005, Morris and Sinclair, by using a flow
argument, have shown that the mixing time of this Markov chain is
$\mathcal{O}(n^{9/2+\epsilon})$, for any $\epsilon > 0$. By using a canonical
path argument on the distributive lattice structure of the set of solutions, we
obtain an improved bound, the mixing time is given as $\tau_{_{x}}(\epsilon)
\leq n^{3} \ln (16 \epsilon^{-1})$.
