Multidimensional Access Methods: Trees Have Grown Everywhere.

Timos K. Sellis, Nick Roussopoulos, Christos Faloutsos: Multidimensional Access Methods: Trees Have Grown Everywhere. VLDB 1997: 13-14
  author    = {Timos K. Sellis and
               Nick Roussopoulos and
               Christos Faloutsos},
  editor    = {Matthias Jarke and
               Michael J. Carey and
               Klaus R. Dittrich and
               Frederick H. Lochovsky and
               Pericles Loucopoulos and
               Manfred A. Jeusfeld},
  title     = {Multidimensional Access Methods: Trees Have Grown Everywhere},
  booktitle = {VLDB'97, Proceedings of 23rd International Conference on Very
               Large Data Bases, August 25-29, 1997, Athens, Greece},
  publisher = {Morgan Kaufmann},
  year      = {1997},
  isbn      = {1-55860-470-7},
  pages     = {13-14},
  ee        = {db/conf/vldb/SellisRF97.html},
  crossref  = {DBLP:conf/vldb/97},
  bibsource = {DBLP,}


This paper is a survey of work and issues on multi-dimensional search trees. We provide a classification of such methods, we describe the related algorithms, we present performance analysis efforts, and finally outline future research directions.

Multi-dimensional search trees and Spatial Access Methods, in general, are designed to handle spatial objects, like points, line segments, polygons, polyhedra etc. The goal is to support spatial queries, such as nearest neighbors queries (find all cities within 10 miles from Washington D.C.), or range queries (find all the lakes on earth, within 30 and 40 degrees of latitude), and so on. The applications are numerous, including traditional database multi-attribute indexing, Geographic Information Systems and spatial database systems, and indexing multimedia databases by content. From the spatial databases viewpoint we can distinguish between two major classes of access methods:

Efficient access methods for point objects (PAMs) include: the LSD-tree, the hB-tree, the Buddy-tree and the TV-tree. All these structures use a hierarchical directory and a set of buckets where all data objects are stored. In Spatial Access Methods (known as SAMs), the fundamental idea for spatial indexing of non-point objects is the use of approximations. In other words, the index handles simple approximations of the actual objects index rather than their actual geometry. The most common approximation used by the majority of existing SAMs is the Minimum Bounding Rectangle (MBR) of the object, i.e., the minimum rectangle with sides parallel to the axes that totally encloses it.

Existing proposals for SAMs are grouped in three different techniques to organize spatial objects.

In the full paper we provide an overview of algorithms that are used to answer point/range queries (further subdivided to intersection and containment) on tree search structures, nearest-neighbor queries, as well as more advanced operations such as spatial joins and direction queries (e.g. find all objects north of another, etc.) In addition, we provide results on the performance of the methods, based on either the mathematical analysis of their behaviour or the experimental use of them.

Having reached a maturity level, multi-dimensional search trees are incorporated into products: linear quadtrees are used in the TIGER system of the U.S. Bureau of Census; R-trees are included in Informix/Illustra in the form of Spatial DataBlades, to name a few.

What is interesting also to note after more than a decade of research and development in the area of multi-dimensional search trees and access methods, is the numerous proposals for using such structures in other than the traditional spatial database applications they were initially proposed for. We have seen multidimensional methods being used to index rules in active database systems, to index multimedia databases by content, to support OLAP and DataCube processing, to index time sequences, and many other novel applications.

Some of the issues that we see being examined in the future include:

Benchmarking. Provide the designers community with statistically well founded workloads sufficient for a variety of benchmarking applications. Such an environment should at least include: a rich database with several real and synthetic datasets, an attractive user interface for user-benchmark communication and a set of tools for visualisation and statistical processing of access methods.

Performance Evaluation of Access Methods. A thorough experimental examination of the various approaches is mandatory, in order to guarantee the nice behavior of the organization under real workloads. This suggests the evaluation of the approaches with real datasets and realistic query types, which will be components of a benchmarking environment. Several criteria for "blind" performance evaluation should be present: common assumptions (e.g. about hardware parameters), extensibility (i.e., support of a wide range of queries) and scalability (i.e., comparison on growing volumes of data) among others.

Query Optimization. The optimization of composite procedure execution is an important issue, which constitutes a relatively undeveloped field in the research area of spatial databases. The term "optimization", although commonly used, is a misnomer, because in many cases (especially in non- conventional DBMSs, like geographic DBMSs) the execution strategy chosen by the DBMS is not the optimal strategy; it is just a reasonably efficient strategy for executing a sequence of operations. The use of heuristics rules for ordering the operations in a procedure execution strategy, as well as the use of systematic cost estimates of the cost of different execution strategies must be further exploited.

There is no question that trees have grown everywhere and will continue to grow in areas where high performance is needed, marking yet another strong contribution from the area of database systems.

Copyright © 1997 by the VLDB Endowment. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the VLDB copyright notice and the title of the publication and its date appear, and notice is given that copying is by the permission of the Very Large Data Base Endowment. To copy otherwise, or to republish, requires a fee and/or special permission from the Endowment.

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Matthias Jarke, Michael J. Carey, Klaus R. Dittrich, Frederick H. Lochovsky, Pericles Loucopoulos, Manfred A. Jeusfeld (Eds.): VLDB'97, Proceedings of 23rd International Conference on Very Large Data Bases, August 25-29, 1997, Athens, Greece. Morgan Kaufmann 1997, ISBN 1-55860-470-7
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Referenced by

  1. Aristides Gionis, Piotr Indyk, Rajeev Motwani: Similarity Search in High Dimensions via Hashing. VLDB 1999: 518-529
  2. Joseph M. Hellerstein, Lisa Hellerstein, George Kollios: On the Generation of 2-Dimensional Index Workloads. ICDT 1999: 113-130
  3. Rasa Bliujute, Christian S. Jensen, Simonas Saltenis, Giedrius Slivinskas: R-Tree Based Indexing of Now-Relative Bitemporal Data. VLDB 1998: 345-356
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