A dynamic stabbing-max data structure with sub-logarithmic query time

Authors:
Yakov Nekrich
Affiliations:
Department of Computer Science, University of Chile, Chile
Venue:
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Year:
2011

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Abstract

In this paper we describe a dynamic data structure that answers one-dimensional stabbing-max queries in optimal O(logn/loglogn) time. Our data structure uses linear space and supports insertions and deletions in O(logn) and O(logn/loglogn) amortized time respectively. We also describe a O(n(logn/loglogn)d−1) space data structure that answers d-dimensional stabbing-max queries in O( (logn/loglogn)d) time. Insertions and deletions are supported in O((logn/loglogn)dloglogn) and O((logn/loglogn)d) amortized time respectively.