Range updates and range sum queries on multidimensional points with monoid weights

Let P be a set of n points in Rd where each point p∈P carries a weight drawn from a commutative monoid (M,+,0). Given a d-rectangle rupd (i.e., an orthogonal rectangle in Rd) and a value Δ∈M, a range update adds Δ to the weight of every point p∈P∩rupd; given a d-rectangle rqry, a range sum query ret...

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Bibliographic Details
Published inComputational geometry : theory and applications Vol. 115; p. 102030
Main Authors Lu, Shangqi, Tao, Yufei
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2023
Subjects
Data structures
Lower bounds
Range sum queries
Range updates
Lower bounds
Data structures
Range updates
Range sum queries
Online AccessGet full text
ISSN0925-7721
DOI10.1016/j.comgeo.2023.102030

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Summary:Let P be a set of n points in Rd where each point p∈P carries a weight drawn from a commutative monoid (M,+,0). Given a d-rectangle rupd (i.e., an orthogonal rectangle in Rd) and a value Δ∈M, a range update adds Δ to the weight of every point p∈P∩rupd; given a d-rectangle rqry, a range sum query returns the total weight of the points in P∩rqry. The goal is to store P in a structure to support updates and queries with attractive performance guarantees. We describe a structure of O˜(n) space that handles an update in O˜(Tupd) time and a query in O˜(Tqry) time for arbitrary functions Tupd(n) and Tqry(n) satisfying Tupd⋅Tqry=n. The result holds for any fixed dimensionality d≥2. Our query-update tradeoff is tight up to a polylog factor subject to the OMv-conjecture.
ISSN:0925-7721
DOI:10.1016/j.comgeo.2023.102030