**Authors:** Bin Fu, Richard Beigel, and Frank Zhou

**Abstract:**
We design volume-efficient molecular algorithms for all problems in
#P, using only reasonable biological operations. In particular, we
give a polynomial-time *O*(2^{n} *n*^{2}
log^{2}*n*)-volume algorithm to compute the number of Hamiltonian
paths in an *n*-node graph. This improves Adleman's celebrated
*n!*-volume algorithm for finding a single Hamiltonian path.