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Recent advances in digital microfluidics have enabled droplet-based biochip devices for DNA sequencing, immunoassays, clinical chemistry, and protein crystallization. Since cross-contamination between droplets of different biomolecules can lead to erroneous outcomes for bioassays, the avoidance of cross-contamination during droplet routing is a key design challenge for biochips. We propose a droplet-routing method that avoids cross-contamination in the optimization of droplet flow paths. The proposed approach targets disjoint droplet routes and synchronizes wash-droplet routing with functional droplet routing, in order to reduce the duration of droplet routing while avoiding the cross-contamination between different droplet routes. In order to avoid cross-contamination between successive routing steps, an optimization technique is used to minimize the number of wash operations that must be used between successive routing steps. Two real-life biochemical applications are used to evaluate the proposed droplet-routing methods.