Efficient processing of aggregated range queries on two-dimensional grids is a common requirement in information retrieval and data mining systems, for example in Geographic Information Systems and OLAP cubes. We introduce a technique to represent grids supporting aggregated range queries that requires little space when the data points in the grid are clustered, which is common in practice. We show how this general technique can be used to support two important types of aggregated queries, which are ranked range queries and counting range queries. Our experimental evaluation shows that this technique can speed up aggregated queries up to more than an order of magnitude, with a small space overhead. HighlightsSpace-efficient representation for two-dimensional grids.Efficient support for aggregated range queries.Proved performance in main memory.Results competitive with the state of the art.Applications to several domains: Geographic Information Systems, OLAP cubes, etc.
@cite_12 introduce compact data structures for various queries on two-dimensional weighted points, including range top- @math queries and range counting queries. Their solutions are based on wavelet trees. For range top- @math queries, the bitmap of each node of the wavelet tree is enhanced as follows: Let @math be the points represented at a node, and @math be the weight of point @math . Then, a RMQ data structure built on @math is stored together with the bitmap. Such a structure uses @math bits and finds the maximum weight in any range @math in constant time @cite_30 and without accessing the weights themselves. Therefore, the total space becomes @math bits.
@cite_30 @cite_12
2007791040 2080990114
Given a static array of @math totally ordered objects, the range minimum query problem is to build a data structure that allows us to answer efficiently subsequent on-line queries of the form “what is the position of a minimum element in the subarray ranging from @math to @math ?”. We focus on two settings, where (1) the input array is available at query time, and (2) the input array is available only at construction time. In setting (1), we show new data structures (a) of size @math bits and query time @math for any positive integer function @math for an arbitrary constant @math , or (b) with @math bits and @math query time, where @math denotes the empirical entropy of @math th order of the input array. In setting (2), we give a data structure of size @math bits and query time @math . All data structures can be constructed in linear time and almost in-place. We consider various data-analysis queries on two-dimensional points. We give new space time tradeoffs over previous work on geometric queries such as dominance and rectangle visibility, and on semigroup and group queries such as sum, average, variance, minimum and maximum. We also introduce new solutions to queries less frequently considered in the literature such as two-dimensional quantiles, majorities, successor predecessor, mode, and various top-k queries, considering static and dynamic scenarios.