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SIAM Journal on Computing
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Range mode and range median queries in constant time and sub-quadratic space
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Range Quantile Queries: Another Virtue of Wavelet Trees
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Improved bounds for range mode and range median queries
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Range selection and median: tight cell probe lower bounds and adaptive data structures
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Dynamic range selection in linear space
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
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ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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Theoretical Computer Science
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In this paper we design data structures supporting range median queries, i.e. report the median element in a sub-range of an array. We consider static and dynamic data structures and batched queries. Our data structures support range selection queries, which are more general, and dominance queries (range rank). In the static case our data structure uses linear space and queries are supported in O(logn/loglogn) time. Our dynamic data structure uses O(nlogn/loglogn) space and supports queries and updates in O((logn/loglogn)2) time.