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Reviewer: Don Goelman

This book provides a synthesis of the two major topics in computing which appear in its title. As the author notes, most students make their acquaintance with data structures without seeing their application to problems in network optimization. On the other hand, most literature on networks, especially the classical literature, does not include a description of the various data structures, and an analysis of their complexities, which may be used to support the network algorithms. The book is a survey of major results, many of them due to the author. It is organized into nine chapters, but there is a natural division between the first five and the last four. The earlier chapters provide the necessary background data structures for the results in network theory discussed in the later chapters. The chapters on data structures are: (1) Foundations, (2) Disjoint Sets, (3) Heaps, (4) Search Trees, and (5) Linking and Cutting Trees. The spirit here is distinctly ADT (Abstract Data Types), with the various structures defined via the operations they support. Some complexity results are mentioned and used without proof; in these cases the author refers to specific entries in the very complete bibliography. In other cases, especially when the results are new or due to the author, the details are included. The chapters on network theory are: (6) Minimum Spanning Trees, (7) Shortest Paths, (8) Network Flows, and (9) Matchings. The setting here is graph theory, rather than linear programming or matroid theory. The author is thus able to use the structures from the earlier part of the book to develop the major results of network optimization; this development shows some important relationships among the different results. In addition, the historical background is often discussed. Because there is quite a bit of terminology, readers should have some experience with data structures and analysis of algorithms, although it is not necessary to have seen these particular structures. Readers who are unfamiliar with the problems of network optimization will still find the descriptions here accessible and the results interesting, while those who are so familiar will enjoy the unified treatment of these results, together with the underlying data structures. A particularly suitable audience would be an advanced seminar of students who have taken basic courses in data structures and classical linear programming and optimization. Both the results themselves and their presentation are aesthetically pleasing. The figures, in particular, help the reader trace the algorithms. The physical presentation of the chapters and their subsections is well organized and laid out. At times the treatment of the different data structures seems episodic, but this impression fades as the various structures reappear to support the later network developments. The Bibliography is one of the strongest features the book has to offer. It contains a complete list of both the classical and modern literature. Besides the full bibliography at the end, there are also bibliographies by chapter, to which the citations within the chapter refer. This is Volume 44 in the CBMS-NSF Regional Conference Series in Applied Mathematics. The author is planning a comprehensive two-volume set on data structures and graph algorithms, which will include the material in the current book.