New Bounds for Range Closest-Pair Problems

Given a dataset S of points in $${\mathbb {R}}^2$$ , the range closest-pair (RCP) problem aims to preprocess into data structure such that when query X is specified, $$S \cap X$$ can be reported efficiently. The RCP viewed as range-search version classical problem, and finds applications many areas. Due its non-decomposability, much more challenging than traditional problems. This paper revisits proposes new structures for various types including quadrants, strips, rectangles, halfplanes. Both worst-case average-case analyses (in sense are drawn uniformly independently from unit square) applied these structures, which result bounds problem. Some significantly improve previous results, while others entirely new.