Partial match queries in quad-K-d trees
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Cita com:
hdl:2117/377538
Tipus de documentText en actes de congrés
Data publicació2022
EditorSchloss Dagstuhl - Leibniz-Zentrum für Informatik
Condicions d'accésAccés obert
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continguts d'aquesta obra estan subjectes a la llicència de Creative Commons
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Reconeixement 4.0 Internacional
Abstract
Quad-K-d trees [Bereckzy et al., 2014] are a generalization of several well-known hierarchical Kdimensional data structures. They were introduced to provide a unified framework for the analysis
of associative queries and to investigate the trade-offs between the cost of different operations and
the memory needs (each node of a quad-K-d tree has arity 2
m for some m, 1 ≤ m ≤ K). Indeed,
we consider here partial match – one of the fundamental associative queries – for several families of
quad-K-d trees including, among others, relaxed K-d trees and quadtrees. In particular, we prove
that the expected cost of a random partial match Pˆn that has s out of K specified coordinates in a
random quad-K-d tree of size n is Pˆn ∼ β · n
α where α and β are constants given in terms of K
and s as well as additional parameters that characterize the specific family of quad-K-d trees under
consideration. Additionally, we derive a precise asymptotic estimate for the main order term of Pn,q
– the expected cost of a fixed partial match in a random quad-K-d tree of size n. The techniques and
procedures used to derive the mentioned costs extend those already successfully applied to derive
analogous results in quadtrees and relaxed K-d trees; our results show that the previous results are
just particular cases, and states the validity of the conjecture made in [Duch et al., 2016] to a wider
variety of multidimensional data structures.
CitacióDuch, A.; Martinez, C. Partial match queries in quad-K-d trees. A: International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms. "33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, AofA 2022: June 20-24, 2022, Philadelphia, PA, USA". Wadern: Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022, p. 8:1-8:16. ISBN 978-3-95977-230-3. DOI 10.4230/LIPIcs.AofA.2022.8.
ISBN978-3-95977-230-3
Versió de l'editorhttps://drops.dagstuhl.de/opus/volltexte/2022/16094/
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