License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2022.57
URN: urn:nbn:de:0030-drops-173427
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17342/
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Lu, Shangqi ; Tao, Yufei

Range Updates and Range Sum Queries on Multidimensional Points with Monoid Weights

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LIPIcs-ISAAC-2022-57.pdf (0.9 MB)

Abstract

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.

BibTeX - Entry

@InProceedings{lu_et_al:LIPIcs.ISAAC.2022.57,
  author =	{Lu, Shangqi and Tao, Yufei},
  title =	{{Range Updates and Range Sum Queries on Multidimensional Points with Monoid Weights}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{57:1--57:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/17342},
  URN =		{urn:nbn:de:0030-drops-173427},
  doi =		{10.4230/LIPIcs.ISAAC.2022.57},
  annote =	{Keywords: Range Updates, Range Sum Queries, Data Structures, Lower Bounds}
}

Keywords: Range Updates, Range Sum Queries, Data Structures, Lower Bounds
Collection: 33rd International Symposium on Algorithms and Computation (ISAAC 2022)
Issue Date: 2022
Date of publication: 14.12.2022

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