An Õ(2n) volume molecular algorithm for Hamiltonian path

We design volume-efficient molecular algorithms for all problems in #P, using only reasonable biological operations. In particular, we give a polynomial-time O(2nn2 log2 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.