2026-07-22T21:25:27Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:17342 2024-03-06T10:59:30Z ddc:004 open_access

Range Updates and Range Sum Queries on Multidimensional Points with Monoid Weights Lu, Shangqi Tao, Yufei Range Updates Range Sum Queries Data Structures Lower Bounds Let P be a set of n points in ℝ^d where each point p ∈ P carries a weight drawn from a commutative monoid (ℳ, +, 0). Given a d-rectangle r_upd (i.e., an orthogonal rectangle in ℝ^d) and a value Δ ∈ ℳ, a range update adds Δ to the weight of every point p ∈ P∩ r_upd; given a d-rectangle r_qry, a range sum query returns the total weight of the points in P ∩ r_qry. The goal is to store P in a structure to support updates and queries with attractive performance guarantees. We describe a structure of Õ(n) space that handles an update in Õ(T_upd) time and a query in Õ(T_qry) time for arbitrary functions T_upd(n) and T_qry(n) satisfying T_upd ⋅ T_qry = 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Shangqi Lu and Yufei Tao 2022 Is Part Of LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ISAAC.2022.57 urn:nbn:de:0030-drops-173427 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.57 eng https://creativecommons.org/licenses/by/4.0/legalcode