Two-dimensional range successor in optimal time and almost linear space

In this article, we revisit the problem of supporting two-dimensional range successor queries. We present a data structure with O (n lglg n) words of space and O(lglgn) query time. This improves the work of Nekrich and Navarro (2012) by a factor of lg lgn in query time, or a factor of lg(is an element of) in space cost, where E is an arbitrary positive constant. Our data structure matches the state of the art for two-dimensional range emptiness queries and achieves the optimal query time. This structure has fruitful applications in computational geometry and text indexing. (C) 2015 Elsevier B.V. All rights reserved.