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- W2398155836 abstract "Let S be a set of n points in d dimensions such that each point is assigned a color. Given a query range Q = a 1 , b 1 ] i? a 2 , b 2 ] i? ? i? a d , b d ] , the geometric range mode query problem asks to report the most frequent color (i.e., a mode) of the multiset of colors corresponding to points in S ? Q . When d = 1 , Chan et al. (2012) 1] gave a data structure that requires O ( n + ( n / Δ ) 2 / w ) words and supports range mode queries in O ( Δ ) time for any Δ ? 1 , where w = ? ( log ? n ) is the word size. Chan et al.?also proposed a data structures for higher dimensions (i.e., d ? 2 ) with O ( s n + ( n / Δ ) 2 d ) words and O ( Δ ? t n ) query time, where s n and t n denote the space and query time of a data structure that supports orthogonal range counting queries on the set S . In this paper we show that the space can be improved without any increase to the query time, by presenting an O ( s n + ( n / Δ ) 2 d / w ) -word data structure that supports orthogonal range mode queries on a set of n points in d dimensions in O ( Δ ? t n ) time, for any Δ ? 1 . When d = 1 , these space and query time costs match those achieved by the current best known one-dimensional data structure." @default.
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- W2398155836 date "2014-01-01" @default.
- W2398155836 modified "2023-09-26" @default.
- W2398155836 title "Low Space Data Structures for Geometric Range Mode Query." @default.
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