Using three-dimensional microfluidic networks for solving computationally hard problems

This paper describes the design of a parallel algorithm that uses moving fluids in a three-dimensional microfluidic system to solve a nondeterministically polynomial complete problem (the maximal clique problem) in polynomial time. This algorithm relies on (i) parallel fabrication of the microfluidic system, (ii) parallel searching of all potential solutions by using fluid flow, and (iii) parallel optical readout of all solutions. This algorithm was implemented to solve the maximal clique problem for a simple graph with six vertices. The successful implementation of this algorithm to compute solutions for small-size graphs with fluids in microchannels is not useful, per se, but does suggest broader application for microfluidics in computation and control.