Fast evaluation of union-intersection expressions

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dc.creatorBille, Philip
dc.creatorPagh, Anna
dc.creatorPagh, Rasmus
dc.date2007-08-23
dc.date.accessioned2026-07-07T08:25:21Z
dc.date.available2026-07-07T08:25:21Z
dc.descriptionWe show how to represent sets in a linear space data structure such that expressions involving unions and intersections of sets can be computed in a worst-case efficient way. This problem has applications in e.g. information retrieval and database systems. We mainly consider the RAM model of computation, and sets of machine words, but also state our results in the I/O model. On a RAM with word size $w$, a special case of our result is that the intersection of $m$ (preprocessed) sets, containing $n$ elements in total, can be computed in expected time $O(n (\log w)^2 / w + km)$, where $k$ is the number of elements in the intersection. If the first of the two terms dominates, this is a factor $w^{1-o(1)}$ faster than the standard solution of merging sorted lists. We show a cell probe lower bound of time $Ω(n/(w m \log m)+ (1-\tfrac{\log k}{w}) k)$, meaning that our upper bound is nearly optimal for small $m$. Our algorithm uses a novel combination of approximate set representations and word-level parallelism.
dc.identifierhttps://arxiv.org/abs/0708.3259
dc.identifierhttp://arxiv.org/abs/0708.3259
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/136625
dc.subjectData Structures and Algorithms
dc.subjectDatabases
dc.subjectInformation Retrieval
dc.titleFast evaluation of union-intersection expressions
dc.typetext

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