On the complexity of design tasks for Digital Microfluidic Biochips

In recent years, a wide range of heuristic as well as exact approaches has been proposed to solve these problems. While the NP-completeness of routing and pin assignment has already been conjectured in the literature, we present the first actual proofs. Thus, the use of general-purpose approaches like SAT solvers is indeed justified. We additionally prove the NP-completeness for variants of the routing problem.