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Given a spatial graph and a set of node attributes, the Node-attributed Spatial Graph Partitioning (NSGP) problem partitions a node-attributed spatial graph into homogeneous sub-graphs that minimize both the total 1 and-while meeting a size constraint on the sub-graphs. 1 is the Root Mean Square Error between a matrix and its rank-one decomposition. The NSGP problem is important for many societal applications such as identifying homogeneous communities in a spatial graph and detecting interrelated patterns in traffic accidents. This problem is NP-hard; it is computationally challenging because of the large size of spatial graphs and the constraint that the sub-graphs must be homogeneous, i.e. similar in terms of node attributes. This paper proposes a novel approach for finding a set of homogeneous sub-graphs that can minimize both the total 1 and-while meeting the size constraint. Experiments and a case study using U.S. Census datasets and HP#6 watershed network datasets demonstrate that the proposed approach partitions a spatial graph into a set of homogeneous sub-graphs and reduces the computational cost.

Given a spatial network and a set of service center nodes from k different resource types, a Multiple Resource-Network Voronoi Diagram (MRNVD) partitions the spatial network into a set of Service Areas that can minimize the total cycle distances of graph-nodes to allotted k service center nodes with different resource types. The MRNVD problem is important for critical societal applications such as assigning essential survival supplies (e.g., food, water, gas, and medical assistance) to residents impacted by man-made or natural disasters. The MRNVD problem is NP-hard; it is computationally challenging due to the large size of the transportation network. Previous work is limited to a single or two different types of service centers, but cannot be generalized to deal with k different resource types. We propose a novel approach for MRNVD that can efficiently identify the best routes to obtain the k different resources. Experiments and a case study using real-world datasets demonstrate that the proposed approach creates MRNVD and significantly reduces the computational cost.