Abstract
In this article, we revisit the problem of supporting two-dimensional range successor queries. We present a data structure with O(nlglgn) words of space and O(lglgn) query time. This improves the work of Nekrich and Navarro (2012) by a factor of lglgn in query time, or a factor of lgϵn in space cost, where ϵ 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.
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