Solving minimum-cost flow problems by successive approximation
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
Finding minimum-cost circulations by canceling negative cycles
Journal of the ACM (JACM)
Finding minimum-cost circulations by successive approximation
Mathematics of Operations Research
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
A faster strongly polynomial minimum cost flow algorithm
Operations Research
An efficient implementation of a scaling minimum-cost flow algorithm
Journal of Algorithms
Combinatorial optimization
Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems
Journal of the ACM (JACM)
Network Flows and Matching: First DIMACS Implementation Challenge
Network Flows and Matching: First DIMACS Implementation Challenge
Generalized network Voronoi diagrams: Concepts, computational methods, and applications
International Journal of Geographical Information Science
Combinatorial Optimization: Theory and Algorithms
Combinatorial Optimization: Theory and Algorithms
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Given a graph and a set of service centers, 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 distances (min-sum) 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 NP-hard; it is computationally challenging because of the large size of the transportation network and the constraint that Service Areas (SAs) must be contiguous in the graph to simplify communication of allotments. Previous work has focused on honoring either service center capacity constraints (e.g., min-cost flow) or service area contiguity (e.g., Network Voronoi Diagrams), but not both. We propose a novel Pressure Equalizer (PE) approach for CCNVD to meet the capacity constraints of service centers while maintaining the contiguity of service areas. Experiments and a case study using post-hurricane Sandy scenarios demonstrate that the proposed algorithm has comparable solution quality to min-cost flow in terms of min-sum; furthermore it creates contiguous service areas, and significantly reduces computational cost.