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Reviewer: Hector Yee

Probably one of the most information-dense books I have ever read, this book provides an extremely detailed treatment of multidimensional data structures. The book goes way beyond your ordinary account of octrees and quadtrees. I have written many such multidimensional data structures as part of my professional career, and yet I found many novel data structures described in the book. The book contains only four chapters. Chapter 1 describes various data structures, such as fixed grids, quadtrees, point quadtree, point-region quadtree, k-dimensional (k-d) trees, grid files, EXCELL, linear hashing, range trees, and priority search trees. After each section, exercises are given to test the reader';s understanding of the material. These data structures are suited for rapidly finding points inside the data structure. Chapter 2 covers different cell types (such as hexagonal versus the normal cubic), and various kinds of traversal orders (such as row order, Morton order, and Peano-Hilbert space filling curves). The chapter also covers binary space partitioning (BSP) trees, winged-edged data structures, and boundary representations such as the matrix (MX) quadtree, MX octree, polygonal map (PM) quadtree, and PM octree. These data structures are good for representing boundaries, such as font outlines. Chapter 3 covers segment trees, interval trees, and priority search trees for rectangles and intervals. These data structures are more suited for sweeping planes toward geometric objects inside the data structure. Chapter 4 covers incremental nearest-neighbor algorithms, and data structures such as the vantage point (vp) tree, generalized hyperplane (gh) tree, and Merkle B (mb) tree. This book is more suited to computer scientists and graduate computer science students than graphics engineers. I have had extensive experience as a graphics engineer, in games and feature animation, and I found this book to be very dense and difficult to understand at parts. Perhaps the terminology is geared toward practitioners of geographic information systems (GIS), but I was unfamiliar with many of the terms used in the book, and it differs from what one would find in typical SIGGRAPH papers. It is certainly not a quick reference, and to appreciate it to its fullest one would have to digest it over a period of time. Other than its academic orientation and its steep technical requirements for understanding, the book has very detailed figures and diagrams that aid in comprehension. I would recommend it as a source of interesting ideas when writing your own data structures, but readers should keep in mind that it is not an easy quick-fix reference. It is also more theoretical than practical in nature (for example, in terms of algorithm analysis). As an engineer, I tend to prefer books of the latter type [1].

Reviewer: Raphael M. Malyankar

This is an ambitious attempt by Hanan Samet, a well-known expert in the field of spatial data indexing, to provide a modern, comprehensive text on multidimensional data representation methods. It is notable for the breadth and depth of its coverage and for the clarity of its treatment of the topics it addresses. Metric spaces are sets for which a distance function between elements is defined; the function qualifies as a metric by obeying the requirements of non-negativity, identity of indiscernibles, symmetry, and the triangle inequality. Multidimensional data and metric spaces are features of several application domains, ranging from the obvious, such as geographical information systems (GIS), to the less obvious, such as data mining and document or image retrieval. Samet has set out to collect and organize a significant portion of the vast amount of research in representation and indexing methods for such data in a text suitable for self-study and college courses. He has done an admirable job. Four chapters make up the bulk of this book. Three of them are substantial enough that they could have been divided into additional chapters. Chapter 1 deals with point data representations. Most of this chapter is devoted to sections on quadtree, k-dimensional tree (k-d tree), and bucket-based approaches, with an additional section on the relatively specialized pyramid k-instantiable tree (PK-tree) method. Shorter sections in this chapter deal with range trees and priority search trees. Chapter 2 addresses representations of objects using various image-based and object-based approaches. The two main subdivisions of this chapter deal with various kinds of interior-based (volumetric) and boundary-based representations. A third, shorter subdivision of this chapter deals with data compaction. Chapter 3, the shortest chapter, discusses structures for interval and small-rectangle data. This somewhat specialized subject is useful in certain application areas such as very large-scale integration (VSLI) design. Chapter 4 covers representations for data in high-dimensional spaces. Such data is a feature of several areas of current interest, such as data mining, document and image search, and retrieval problems. This chapter covers an eclectic collection of approaches and representations, tied together by the fact that they are designed for representing data defined in spaces with a relatively high number of dimensions. Chapters 1 and 2 are what one would expect to find in a book of this nature. Chapters 3 and 4 are significant additions, especially chapter 4, which is an excellent and substantial collection of topics of particular interest for currently active research and development in diverse areas of research and praxis, such as Web search engines. Within each subarea, the coverage of specific topics described is as one would expect, given the book's subject area; in other words, I found described, in more or less detail, the topics I expected, plus a few more. Implementation issues are often discussed, but are not a major focus of this book. Exercises are provided at the conclusion of each topic, which usually means after most sections and subsections, and often after smaller subdivisions of the text. Four appendices follow the main chapters. Appendix A contains a review of and notes on B-trees and their relations, while Appendices B and C survey linear and spiral hashing. The fourth appendix contains a brief overview of the pseudocode language used for describing algorithms and notes for anyone trying to implement them in code. Solutions to most of the exercises follow in an extensive section. The bibliography consists of more than 2,000 entries. A reference keyword index follows, which can be used to find relevant literature other than that cited in the text. Since the exposition in this book is?understandably and appropriately?tutorial-directed (that is, aimed at conveying the concepts rather than reporting research), the reader who desires more detail should find this keyword index a valuable time-saving aid to looking up sources in addition to those cited. An author index and subject index are also included. The explanations are generally clear, and numerous well-drawn and informative figures accompany the text. The layout of the material is well planned and executed. Visually, this is an easy book to read. Nevertheless, it is not a book that can be read quickly or skimmed, because the concepts are sometimes quite complex, and the information density is usually quite high. Careful reading and frequent pauses for critical thinking and assimilation of the points made by the author are necessary, especially since there are a few small mistakes even in this generally excellent text. For example, in section 4.4.2 the two-dimensional (2D) and three-dimensional (3D) examples at the end of the first paragraph are not entirely accurate as stated (an illustration in the margin here would have made this clear instantly). Topic tags in the margin, demarcating successive topics, might have improved understandability and helped the reader organize concepts in a few places, such as section 1.5.1.4, which discusses variants of k-d trees, and some subdivisions of section 4.6, which addresses dimension reduction methods for indexing high-dimensional data. A minor but useful feature is the ample space allotted to margins, which have plenty of room for the reader's own annotations. As the author notes, there is ample material in this book for an advanced graduate-level course in data structures, and a carefully selected set of topics would also be suitable for an upper-level undergraduate course (the preface provides some suggestions). Select material would also be suitable supplemental reading for courses in computer graphics, programming for computer games, databases, and perhaps geographic information systems and information retrieval. The intended audience also includes readers engaging in independent study of the subject area or selected topics from it, for which purpose the expository quality and nature of the exercises make this book admirably suited. Readers who wish to make the most of the material will find a knowledge of data structures and algorithms to be essential, at a minimum to the level of an undergraduate data structures course or the equivalent. Exposure to certain mathematical and statistical concepts will be needed to get the most out of a few sections, for example, principal component analysis or singular value decomposition (SVD) for part of the section on "dimension reduction methods" in chapter 4. Your favorite Web search engine, a little diligence, and a spare hour or two will allow anyone with at least college-level or equivalent mathematics to catch up on such topics as necessary. This book is both a good reference and an excellent learning resource¿the kind of volume one keeps handy for repeated consultation. I strongly recommend it to students and practitioners interested in data structures and indexing methods for spatial and multidimensional data. Online Computing Reviews Service