Improved dynamic data structures for unit-disk range reporting: preprocess n planar points so a query disk of fixed radius reports all contained points, under point insertions and deletions. The query time is improved to O(log n + k) (k the output size) with O(n log n) space and unchanged amortized update times, via a new shallow-cutting algorithm for circular arcs. The same techniques give a dynamic unit-disk range-emptiness structure in O(n) space with O(log^1+e n) amortized updates and O(log n) queries. Builds on alpha-hulls, lifting disks to halfspaces, point location, and Voronoi/Delaunay structures.
Haitao Wang and Yiming Zhao (STACS 2025) give improved dynamic data structures for unit-disk range reporting: for n points in the plane and a fixed radius r, preprocess P so that any query disk of ra…