The Skip Quadtree: A Simple Dynamic Data Structure for Multidimensional Data

We present a new multi-dimensional data structure, which we call the skip quadtree (for point data in R^2) or the skip octree (for point data in R^d, with constant d>2). Our data structure combines the best features of two well-known data structures, in that it has the well-defined "box"-shaped regions of region quadtrees and the logarithmic-height search and update hierarchical structure of skip lists. Indeed, the bottom level of our structure is exactly a region quadtree (or octree for higher dimensional data). We describe efficient algorithms for inserting and deleting points in a skip quadtree, as well as fast methods for performing point location and approximate range queries.Comment: 12 pages, 3 figures. A preliminary version of this paper appeared in the 21st ACM Symp. Comp. Geom., Pisa, 2005, pp. 296-30

Partial match queries in relaxed K-dt trees

The study of partial match queries on random hierarchical multidimensional data structures dates back to Ph. Flajolet and C. Puech’s 1986 seminal paper on partial match retrieval. It was not until recently that fixed (as opposed to random) partial match queries were studied for random relaxed K-d trees, random standard K-d trees, and random 2-dimensional quad trees. Based on those results it seemed natural to classify the general form of the cost of fixed partial match queries into two families: that of either random hierarchical structures or perfectly balanced structures, as conjectured by Duch, Lau and Martínez (On the Cost of Fixed Partial Queries in K-d trees Algorithmica, 75(4):684–723, 2016). Here we show that the conjecture just mentioned does not hold by introducing relaxed K-dt trees and providing the average-case analysis for random partial match queries as well as some advances on the average-case analysis for fixed partial match queries on them. In fact this cost –for fixed partial match queries– does not follow the conjectured forms.Peer ReviewedPostprint (author's final draft

Perspects in astrophysical databases

Astrophysics has become a domain extremely rich of scientific data. Data mining tools are needed for information extraction from such large datasets. This asks for an approach to data management emphasizing the efficiency and simplicity of data access; efficiency is obtained using multidimensional access methods and simplicity is achieved by properly handling metadata. Moreover, clustering and classification techniques on large datasets pose additional requirements in terms of computation and memory scalability and interpretability of results. In this study we review some possible solutions

Data Management and Mining in Astrophysical Databases

We analyse the issues involved in the management and mining of astrophysical data. The traditional approach to data management in the astrophysical field is not able to keep up with the increasing size of the data gathered by modern detectors. An essential role in the astrophysical research will be assumed by automatic tools for information extraction from large datasets, i.e. data mining techniques, such as clustering and classification algorithms. This asks for an approach to data management based on data warehousing, emphasizing the efficiency and simplicity of data access; efficiency is obtained using multidimensional access methods and simplicity is achieved by properly handling metadata. Clustering and classification techniques, on large datasets, pose additional requirements: computational and memory scalability with respect to the data size, interpretability and objectivity of clustering or classification results. In this study we address some possible solutions.Comment: 10 pages, Late

Design, Implementation and Preliminary Analysis of General Multidimensional Trees

In this thesis, a new multidimensional data structure, the q-kd tree, for storing points lying in a multidimensional space is defined, implemented and experimentally analyzed. This new data structure has k-d trees and quad-trees as particular cases. The main difference between q-kd trees and either kd-trees or quad-trees is the way in which discriminants are assigned to each node of the tree. While this is fixed for kd-trees and quad-trees, it is variable for q-kd trees. We propose two different ways for assigning discriminants to nodes, the heuristics: Split Tendency and Prob-of-1. These heuristics allow us to build what we call quasi-optimal q-kd trees and randomly-split q-kd trees respectively. Experimentally we show that our variants of q-kd trees are in between quad-trees and k-d trees concerning the memory space and internal path length, and that by proper parameter settings it is possible to construct q-kd trees taylored to the space and time restrictions we can have.Incomin

Design, Implementation and Preliminary Analysis of General Multidimensional Trees

In this thesis, a new multidimensional data structure, the q-kd tree, for storing points lying in a multidimensional space is defined, implemented and experimentally analyzed. This new data structure has k-d trees and quad-trees as particular cases. The main difference between q-kd trees and either kd-trees or quad-trees is the way in which discriminants are assigned to each node of the tree. While this is fixed for kd-trees and quad-trees, it is variable for q-kd trees. We propose two different ways for assigning discriminants to nodes, the heuristics: Split Tendency and Prob-of-1. These heuristics allow us to build what we call quasi-optimal q-kd trees and randomly-split q-kd trees respectively. Experimentally we show that our variants of q-kd trees are in between quad-trees and k-d trees concerning the memory space and internal path length, and that by proper parameter settings it is possible to construct q-kd trees taylored to the space and time restrictions we can have.Incomin