Partial match retrieval of multidimensional data

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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

Performance comparison of point and spatial access methods

In the past few years a large number of multidimensional point access methods, also called multiattribute index structures, has been suggested, all of them claiming good performance. Since no performance comparison of these structures under arbitrary (strongly correlated nonuniform, short "ugly") data distributions and under various types of queries has been performed, database researchers and designers were hesitant to use any of these new point access methods. As shown in a recent paper, such point access methods are not only important in traditional database applications. In new applications such as CAD/CIM and geographic or environmental information systems, access methods for spatial objects are needed. As recently shown such access methods are based on point access methods in terms of functionality and performance. Our performance comparison naturally consists of two parts. In part I we w i l l compare multidimensional point access methods, whereas in part I I spatial access methods for rectangles will be compared. In part I we present a survey and classification of existing point access methods. Then we carefully select the following four methods for implementation and performance comparison under seven different data files (distributions) and various types of queries: the 2-level grid file, the BANG file, the hB-tree and a new scheme, called the BUDDY hash tree. We were surprised to see one method to be the clear winner which was the BUDDY hash tree. It exhibits an at least 20 % better average performance than its competitors and is robust under ugly data and queries. In part I I we compare spatial access methods for rectangles. After presenting a survey and classification of existing spatial access methods we carefully selected the following four methods for implementation and performance comparison under six different data files (distributions) and various types of queries: the R-tree, the BANG file, PLOP hashing and the BUDDY hash tree. The result presented two winners: the BANG file and the BUDDY hash tree. This comparison is a first step towards a standardized testbed or benchmark. We offer our data and query files to each designer of a new point or spatial access method such that he can run his implementation in our testbed

Multidimensional Range Queries on Modern Hardware

Range queries over multidimensional data are an important part of database workloads in many applications. Their execution may be accelerated by using multidimensional index structures (MDIS), such as kd-trees or R-trees. As for most index structures, the usefulness of this approach depends on the selectivity of the queries, and common wisdom told that a simple scan beats MDIS for queries accessing more than 15%-20% of a dataset. However, this wisdom is largely based on evaluations that are almost two decades old, performed on data being held on disks, applying IO-optimized data structures, and using single-core systems. The question is whether this rule of thumb still holds when multidimensional range queries (MDRQ) are performed on modern architectures with large main memories holding all data, multi-core CPUs and data-parallel instruction sets. In this paper, we study the question whether and how much modern hardware influences the performance ratio between index structures and scans for MDRQ. To this end, we conservatively adapted three popular MDIS, namely the R*-tree, the kd-tree, and the VA-file, to exploit features of modern servers and compared their performance to different flavors of parallel scans using multiple (synthetic and real-world) analytical workloads over multiple (synthetic and real-world) datasets of varying size, dimensionality, and skew. We find that all approaches benefit considerably from using main memory and parallelization, yet to varying degrees. Our evaluation indicates that, on current machines, scanning should be favored over parallel versions of classical MDIS even for very selective queries

A limit process for partial match queries in random quadtrees and 22-d trees

We consider the problem of recovering items matching a partially specified pattern in multidimensional trees (quadtrees 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 $n$ points, it is known that the number of nodes $C_n(\xi )$ to visit in order to report the items matching a random query $\xi$, independent and uniformly distributed on $[0,1]$, satisfies $\mathbf {E}[{C_n(\xi )}]\sim\kappa n^{\beta}$, where $\kappa$ and $\beta$ are explicit constants. We develop an approach based on the analysis of the cost $C_n(s)$ of any fixed query $s\in[0,1]$, and give precise estimates for the variance and limit distribution of the cost $C_n(x)$. Our results permit us to describe a limit process for the costs $C_n(x)$ as $x$ varies in $[0,1]$; one of the consequences is that $\mathbf {E}[{\max_{x\in[0,1]}C_n(x)}]\sim \gamma n^{\beta}$; this settles a question of Devroye [Pers. Comm., 2000].Comment: Published in at http://dx.doi.org/10.1214/12-AAP912 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org). arXiv admin note: text overlap with arXiv:1107.223

Location-based indexing for mobile context-aware access to a digital library

Mobile information systems need to collaborate with each other to provide seamless information access to the user. Information about the user and their context provides the points of contact between the systems. Location is the most basic user context. TIP is a mobile tourist information system that provides location-based access to documents in the digital library Greenstone. This paper identifies the challenges for providing effcient access to location-based information using the various access modes a tourist requires on their travels. We discuss our extended 2DR-tree approach to meet these challenges

On the cost of fixed partial match queries in K-d trees

The final publication is available at Springer via http://dx.doi.org/10.1007/s00453-015-0097-4Partial match queries constitute the most basic type of associative queries in multidimensional data structures such as K-d trees or quadtrees. Given a query q=(q0,…,qK-1) where s of the coordinates are specified and K-s are left unspecified (qi=*), a partial match search returns the subset of data points x=(x0,…,xK-1) in the data structure that match the given query, that is, the data points such that xi=qi whenever qi¿*. There exists a wealth of results about the cost of partial match searches in many different multidimensional data structures, but most of these results deal with random queries. Only recently a few papers have begun to investigate the cost of partial match queries with a fixed query q. This paper represents a new contribution in this direction, giving a detailed asymptotic estimate of the expected cost Pn,q for a given fixed query q. From previous results on the cost of partial matches with a fixed query and the ones presented here, a deeper understanding is emerging, uncovering the following functional shape for Pn,q Pn,q=¿·(¿i:qi is specifiedqi(1-qi))a/2·na+l.o.t. (l.o.t. lower order terms, throughout this work) in many multidimensional data structures, which differ only in the exponent a and the constant ¿, both dependent on s and K, and, for some data structures, on the whole pattern of specified and unspecified coordinates in q as well. Although it is tempting to conjecture that this functional shape is “universal”, we have shown experimentally that it seems not to be true for a variant of K-d trees called squarish K-d trees.Peer ReviewedPostprint (author's final draft