Given a graph and a set of service center nodes, a Capacity Constrained Network-Voronoi Diagram (CCNVD) 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 and assigning patients to hospitals. This problem is NPO-hard; it is computationally challenging because of the large size of the transportation network and the constraint that service areas must be contiguous in the graph to simplify communication of allotments. Previous work has focused on honoring either service area contiguity (e.g., Network Voronoi Diagrams) or service center capacity constraints (e.g., min-cost flow), but not both. We introduced a novel Pressure Equalizer (PE) approach for CCNVD to meet the capacity constraints of service centers while maintaining the contiguity of service areas. However, we find that the main bottleneck of the PE algorithm is testing whether service areas are contiguous. We propose novel algorithms that reduce the computational cost. Experiments using road maps from five different regions demonstrate that the proposed approaches significantly reduce computational cost for the PE approach.