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Computational geometry: algorithms and applications
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Incremental distance join algorithms for spatial databases
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Distance browsing in spatial databases
ACM Transactions on Database Systems (TODS)
Closest pair queries in spatial databases
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Influence sets based on reverse nearest neighbor queries
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STR: A Simple and Efficient Algorithm for R-Tree Packing
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Discovery of Influence Sets in Frequently Updated Databases
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iDistance: An adaptive B+-tree based indexing method for nearest neighbor search
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VLDB '05 Proceedings of the 31st international conference on Very large data bases
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SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
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This paper proposes and solves a new problem called spatial matching (SPM). Let P and O be two sets of objects in an arbitrary metric space, where object distances are defined according to a norm satisfying the triangle inequality. Each object in O represents a customer, and each object in P indicates a service provider, which has a capacity corresponding to the maximum number of customers that can be supported by the provider. SPM assigns each customer to her/his nearest provider, among all the providers whose capacities have not been exhausted in serving other closer customers. We elaborate the applications where SPM is useful, and develop algorithms that settle this problem with a linear number O(|P| + |O|) of nearest neighbor queries. We verify our theoretical findings with extensive experiments, and show that the proposed solutions outperform alternative methods by a factor of orders of magnitude.