In the screening of cytological samples, a slide is examined using a microscope. Since the area of the specimen is very large compared with the area of a microscope field of view (FOV), a large number of FOVs is needed to cover the entire specimen area. A heuristic reducing the number of FOVs has been developed to aid in screening these specimens on the automated microscopy workstation. A smear slide is prescreened on a computer-aided optimal microscope system and locations of diagnostically significant material are stored. The heuristic computes a set of FOVs that covers this material and a route between them. As the problem is of large scale and must be solved repeatedly in real time any heuristic must be very fast. Our heuristic solves a set partitioning problem, followed by a traveling salesman problem. It produces a good solution within a very short computing time.