TY - JOUR

T1 - Efficient non-intersection queries on aggregated geometric data

AU - Gupta, Prosenjit

AU - Janardan, Ravi

AU - Smid, Michiel

PY - 2009/12/1

Y1 - 2009/12/1

N2 - Geometric intersection searching problems are a well-studied class of query-retrieval problems with many applications. The goal here is to preprocess a set of geometric objects so that the ones that are intersected by a query object can be reported efficiently. Often, a more general version of the problem arises, where the data comes aggregated in disjoint groups and of interest are the groups, not the individual objects, that are intersected by the query object. One approach to a generalized problem is to ignore the grouping, solve the corresponding classical problem, and then infer the groups from the reported answer. However, this is not efficient, since the number of objects intersected can be much larger than the number of groups (i.e., the output size). The problem of designing efficient, output-sensitive query algorithms for generalized intersection searching has received much attention in recent years, and such solutions have been developed for several problems. This paper considers a new class of generalized query-retrieval problems. Specifically, given aggregated geometric data the goal is to report the distinct groups such that no objects from those groups are intersected by the query. Of interest in these generalized non-intersection searching problems are solutions where the query time is sensitive to the output size, i.e., the number of groups reported. Unfortunately, the obvious approaches of (i) solving the corresponding generalized intersection searching problem and reporting the complement, or (ii) solving a generalized intersection searching problem with the complement of the query are either inefficient or incorrect. This paper provides efficient, output-sensitive solutions to several generalized non-intersection searching problems, using techniques such as geometric duality, sparsification, persistence, filtering search, and pruning.

AB - Geometric intersection searching problems are a well-studied class of query-retrieval problems with many applications. The goal here is to preprocess a set of geometric objects so that the ones that are intersected by a query object can be reported efficiently. Often, a more general version of the problem arises, where the data comes aggregated in disjoint groups and of interest are the groups, not the individual objects, that are intersected by the query object. One approach to a generalized problem is to ignore the grouping, solve the corresponding classical problem, and then infer the groups from the reported answer. However, this is not efficient, since the number of objects intersected can be much larger than the number of groups (i.e., the output size). The problem of designing efficient, output-sensitive query algorithms for generalized intersection searching has received much attention in recent years, and such solutions have been developed for several problems. This paper considers a new class of generalized query-retrieval problems. Specifically, given aggregated geometric data the goal is to report the distinct groups such that no objects from those groups are intersected by the query. Of interest in these generalized non-intersection searching problems are solutions where the query time is sensitive to the output size, i.e., the number of groups reported. Unfortunately, the obvious approaches of (i) solving the corresponding generalized intersection searching problem and reporting the complement, or (ii) solving a generalized intersection searching problem with the complement of the query are either inefficient or incorrect. This paper provides efficient, output-sensitive solutions to several generalized non-intersection searching problems, using techniques such as geometric duality, sparsification, persistence, filtering search, and pruning.

KW - Generalized non-intersection problems

KW - Geometric searching

KW - Output-sensitive querying

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U2 - 10.1142/S0218195909003088

DO - 10.1142/S0218195909003088

M3 - Article

AN - SCOPUS:75149156601

VL - 19

SP - 479

EP - 506

JO - International Journal of Computational Geometry and Applications

JF - International Journal of Computational Geometry and Applications

SN - 0218-1959

IS - 6

ER -