Partial match queries in random quadtrees
Nicolas Broutin, Ralph Neininger, Henning Sulzbach

TL;DR
This paper analyzes the cost of partial match queries in random quadtrees and k-d trees, providing precise estimates and limit distributions for query costs as data size grows.
Contribution
It introduces a new approach analyzing fixed query costs to derive detailed asymptotic behavior and limit processes for partial match query costs in multidimensional trees.
Findings
Expected query cost scales as n^β with explicit constants.
Variance and limit distribution of fixed query costs are characterized.
Maximum query cost over [0,1] scales as γ n^β.
Abstract
We consider the problem of recovering items matching a partially specified pattern in multidimensional trees (quad trees and k-d trees). We assume the traditional model where the data consist of independent and uniform points in the unit square. For this model, in a structure on points, it is known that the number of nodes to visit in order to report the items matching an independent and uniformly on random query satisfies , where and are explicit constants. We develop an approach based on the analysis of the cost of any fixed query , and give precise estimates for the variance and limit distribution of the cost . Our results permit to describe a limit process for the costs as varies in ; one of the consequences is that $E{\max_{x\in [0,1]} C_n(x)} \sim…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
