Finding Range Minima in the Middle: Approximations and Applications

13 years 2 months ago

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Abstract. A Range Minimum Query asks for the position of a minimal element between two speciﬁed array-indices. We consider a natural extension of this, where our further constraint is that if the minimum in a query interval is not unique, then the query should return an approximation of the median position among all positions that attain this minimum. We present a succinct preprocessing scheme using Dn+o(n) bits in addition to the static input array (small constant D), such that subsequent “range median of minima queries” can be answered in constant time. This data structure can be built in linear time, with little extra space needed at construction time. We introduce several new combinatorial concepts such as Super-Cartesian Trees and Super-Ballot Numbers. We give applications of our preprocessing scheme in text indexes such as (compressed) suﬃx arrays and trees. Mathematics Subject Classiﬁcation (2000). Primary 68W05; Secondary 68W25; Tertiary 68R05. Keywords. Range Minimum...

Johannes Fischer, Volker Heun

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