This paper describes the design of a parallel algorithm that uses moving fl
uids in a three-dimensional microfluidic system to solve a nondeterministic
ally polynomial complete problem (the maximal clique problem) in polynomial
time. This algorithm relies on (i) parallel fabrication of the microfluidi
c 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 s
olutions for small-size graphs with fluids in microchannels is not useful,
per se, but does suggest broader application for microfluidics in computati
on and control.