Capacity Constrained Network Voronoi Diagrams - Yang, Kwangsoo; Shekhar, Shashi (Spatial Network Big Databases, 2017)
Network Voronoi Diagrams (NVD) are currently used in various spatial analysis applications, such as finding nearest points of interest. In this chapter, we introduce a special case of NVD, namely the Capacity Constrained Network-Voronoi Diagram (CCNVD) and explore techniques for creating this diagram. Given a graph and a set of service center nodes, a Capacity Constrained Network-Voronoi Diagram partitions the graph into a set of contiguous service areas that meet service center capacities and minimize the sum of the shortest distances from graph-nodes to allotted service centers. The CCNVD problem is important for critical societal applications such as assigning evacuees to shelters or assigning patients to hospitals during emergencies because CCNVD allots routes (e.g., evacuation routes) or limited resource (e.g., gas, water, or shelters) equally, efficiently, and more safely to evacuees (or other clients). One of the biggest challenges in this problem is to minimize the computational cost to construct a CCNVD in an emergency situation. The chapter provides three algorithms to efficiently construct a CCNVD.