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