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Algorithmic aspects of flows in networks
Book Reviews
382
and research workers in all fields where data is analyzed using computers.
J. Sztrik University of Debrecen P.O. Box 10 Debrecen 4010 Hungary
GiJnther Ruhe
Algorithmic Aspects of Flows in Networks Kluwer Academic Publishers, Dordrecht, 1991, viii + 203 pages, Dfl.145.00, ISBN 0792311515 Network optimization was one of the first combinatorial optimization problems studied, beginning with Ford and Fulkerson's work in the late 1950's. Despite its long history, network optimization is still a very active research area, with new and improved algorithms being designed every year. The past five years have been particularly fertile with fundamentally different approaches to network optimization being designed by Goldberg, Goldfarb, Orlin, Tarjan, and many others. This book attempts to review classical and recent results in network optimization. After a very brief introduction to graph theory and complexity, the first network model examined is the maximum flow problem. In addition to the classical algorithms of Dinic and Edmonds and Karp, the author has an extended discussion of the preflow algorithm of Goldberg. Computational results from a paper of Derigs and Meier examine some of the algorithmic choices that can be made. This chapter concludes with a cut tree algorithm of Gusfield. Chapter 3 discusses the minimum-cost flow problem. After a short discussion of some polynomial algorithms, the simplex algorithm is discussed in detail. Computational results from Bertsekas and Tseng compare their relaxation method to Grigoriadis and Hsu's simplex implementation. Chapter 4 covers the generalized network flow (or networks with multipliers) problem. Again, a combinatorial algorithm is discussed (that of Goldberg, Plotkin, and Tardos for maximum generalized flow) followed by an exposition of the
simplex algorithm. The computational results concern only the simplex implementation. Chapter 5, the longest chapter with 44 pages, concerns multicriteria flow while Chapter 6 covers parametric flow. These models are applicable to a wide variety of problems and are less generally known than the models in the preceding chapters. Many of the results in these chapters are not yet published, so this book is a good source for these results. Chapter 7 discusses the possibility of detecting embedded network structure. Finally, Chapter 8 outlines solving networks with additional constraints using the primal basis partitioning technique. This book provides a good coverage of some interesting new developments in network optimization. The writing is serviceable but is not idiomatic and could have used more thorough editing. Another weakness of this book is that the author rarely goes beyond what is available in the literature. In particular, rather than create a new computational experiment, the author simply uses the computational experience of his sources. While this can be adequate in cases where the paper is designed to test implementation possibilities, as for maximum flow and parametric flow, many of his source papers have a quite different agenda. Finally, some major research focuses, like polynomial simplex algorithms in network optimization, are treated sketchily, or not at all. Overall, though, this book provides an interesting and different perspective on a very active field. Michael Trick Graduate School of Industrial Administration Carnegie Mellon University Pittsburgh, PA 15213 USA
Elliot R. Lieberman
Multi-objective Programming in the USSR Academic Press, San Diego, 1991, xxviii + 368 pages, $59.95, ISBN 0-12-449660-1 The book documents the author's attempt to trace, assemble and analyze the development of multi-objective mathematical programming in the
382
and research workers in all fields where data is analyzed using computers.
J. Sztrik University of Debrecen P.O. Box 10 Debrecen 4010 Hungary
GiJnther Ruhe
Algorithmic Aspects of Flows in Networks Kluwer Academic Publishers, Dordrecht, 1991, viii + 203 pages, Dfl.145.00, ISBN 0792311515 Network optimization was one of the first combinatorial optimization problems studied, beginning with Ford and Fulkerson's work in the late 1950's. Despite its long history, network optimization is still a very active research area, with new and improved algorithms being designed every year. The past five years have been particularly fertile with fundamentally different approaches to network optimization being designed by Goldberg, Goldfarb, Orlin, Tarjan, and many others. This book attempts to review classical and recent results in network optimization. After a very brief introduction to graph theory and complexity, the first network model examined is the maximum flow problem. In addition to the classical algorithms of Dinic and Edmonds and Karp, the author has an extended discussion of the preflow algorithm of Goldberg. Computational results from a paper of Derigs and Meier examine some of the algorithmic choices that can be made. This chapter concludes with a cut tree algorithm of Gusfield. Chapter 3 discusses the minimum-cost flow problem. After a short discussion of some polynomial algorithms, the simplex algorithm is discussed in detail. Computational results from Bertsekas and Tseng compare their relaxation method to Grigoriadis and Hsu's simplex implementation. Chapter 4 covers the generalized network flow (or networks with multipliers) problem. Again, a combinatorial algorithm is discussed (that of Goldberg, Plotkin, and Tardos for maximum generalized flow) followed by an exposition of the
simplex algorithm. The computational results concern only the simplex implementation. Chapter 5, the longest chapter with 44 pages, concerns multicriteria flow while Chapter 6 covers parametric flow. These models are applicable to a wide variety of problems and are less generally known than the models in the preceding chapters. Many of the results in these chapters are not yet published, so this book is a good source for these results. Chapter 7 discusses the possibility of detecting embedded network structure. Finally, Chapter 8 outlines solving networks with additional constraints using the primal basis partitioning technique. This book provides a good coverage of some interesting new developments in network optimization. The writing is serviceable but is not idiomatic and could have used more thorough editing. Another weakness of this book is that the author rarely goes beyond what is available in the literature. In particular, rather than create a new computational experiment, the author simply uses the computational experience of his sources. While this can be adequate in cases where the paper is designed to test implementation possibilities, as for maximum flow and parametric flow, many of his source papers have a quite different agenda. Finally, some major research focuses, like polynomial simplex algorithms in network optimization, are treated sketchily, or not at all. Overall, though, this book provides an interesting and different perspective on a very active field. Michael Trick Graduate School of Industrial Administration Carnegie Mellon University Pittsburgh, PA 15213 USA
Elliot R. Lieberman
Multi-objective Programming in the USSR Academic Press, San Diego, 1991, xxviii + 368 pages, $59.95, ISBN 0-12-449660-1 The book documents the author's attempt to trace, assemble and analyze the development of multi-objective mathematical programming in the