Regional Coverage Maximization: Alternative Geographical Space Abstraction and Modeling

Analysis results are often found to vary with the way we abstract geographical space. When continuous geographic phenomena are abstracted, processed, and stored in a digital environment, some level of discretization is often employed. Information loss in a discretization process brings about uncertainty/error, and as a result research findings may be highly dependent on the particular discretization method used. This article examines one spatial problem concerning how to achieve the maximal regional coverage given a limited number of service facilities. Two widely used geographical space abstraction approaches are examined, the point-based representation and the area-based representation, and issues associated with each representation scheme are analyzed. To accommodate the limitations of the existing representation schemes, a mixed representation strategy is proposed along with a new maximal covering model. Experiments are conducted to site warning sirens in Dublin, Ohio. Results demonstrate the effectiveness of the mixed representation scheme in finding high-quality solutions when the regional coverage level is medium or high.