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We describe a new data structure for dynamic nearest neighbor queries in theplane with respect to a general family of distance functions. These include$L_p$-norms and additively weighted Euclidean distances. Our data structuresupports general (convex, pairwise disjoint) sites that have constantdescription complexity (e.g., points, line segments, disks, etc.). Ourstructure uses $O(n \log^3 n)$ storage, and requires polylogarithmic update andquery time, improving an earlier data structure of Agarwal, Efrat and Sharirthat required $O(n^\varepsilon)$ time for an update and $O(\log n)$ time for aquery [SICOMP, 1999]. Our data structure has numerous applications. In all ofthem, it gives faster algorithms, typically reducing an $O(n^\varepsilon)$factor in the previous bounds to polylogarithmic. In addition, we give here twonew applications: an efficient construction of a spanner in a disk intersectiongraph, and a data structure for efficient connectivity queries in a dynamicdisk graph.

Dynamic Planar Voronoi Diagrams for General Distance Functions and their Algorithmic Applications