Abstract

In this article, we revisit the problem of supporting two-dimensional range successor queries. We present a data structure with O(nlg⁡lg⁡n) words of space and O(lg⁡lg⁡n) query time. This improves the work of Nekrich and Navarro (2012) by a factor of lg⁡lg⁡n in query time, or a factor of lgϵ⁡n 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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