Solid phase DNA solution to the Hamiltonian path problem

A solid-phase method for solving the Hamiltonian path problem (HPP) is described. The method employs only fast and simple DNA operations amenable to full automation. Single-stranded DNA molecules representing paths with no city visited twice are synthesized city-by-city from the start city on the surface of a solid support. The solution can thus be found in the computation time proportional to the number of cities. As well as the stepwise path synthesis, a pruning technique developed for the removal of looping paths helps the reduction of DNA molecules necessary for the computation; thus deenitely increasing the size of problems solvable on a DNA-based computer. Experiments using Adleman's seven-city instance of the HPP showed that the path extension cycle was very accurate and took only about 45 min. Our solid-phase method has originally been developed for solving the HPP, but it could also be applied to other problems requiring a massive parallelism in computation.

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