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Minimal cost flow in processing networks: A primal approach
Book Reviews
sign with unknown arc-capacities and 'multiterminal channel routing'. Three papers deal with different problems arising in database theory. One of these provides an interesting study of algorithms to detect strong equivalence--a notion based on the concepts of kernels--of hypergraphs. Another paper presents algorithms for relational data-base processing to be used on VLSI mesh-of-tree processor structures. A systematic analysis of parameters of a special tree-datastructure (trie) and various applications are presented in a third paper. Approximate algorithms have become an important means in attacking NP-complete problems. Three papers deal with such algorithms for k-center, weighted vertex, multiple edge cover and dominating set problems, the maximum clique and set packing problem. One interesting result is that in a certain probabilistic environment the dominating set problem can always be solved asymptotically optimally by a randomly selected feasible solution. Among the graph theoretic papers one study contains an elegant characterization of the relations between the consistency of quadratic boolean equations and the K~nig-Egervfiry property. Especially for those who are working on VLSIchip-design the paper on channel routing of multiterminal nets may be of particular interest. It presents a fast algorithm for wiring multiterminal pin nets in at most three layers of a grid-structured channel, allowing connections (' vias') between different layers while guaranteeing a maximum channel width of at most twice the density of the problem. This book may be of value for all who are working on related topics and especially for those interested in algorithmic aspects of combinatorial optimization.
O. HOLLAND University of Bonn Bonn, Germany, Fed. Rep.
J. K O E N E
Minimal Cost Flow in Processing Networks: A Primal Approach CWI Tract 4, Amsterdam, 1983, iv + 157 pages, Dfl.22.70
257
The main issue of this work is a treatment of primal simplex based procedures for solving processing network problems. By processing network the author means a generalized network where a given flow may split up into several components with given proportions (refining process) or several components may be blended with given proportions (blending process). Such structures occur in production planning, in assembly models, in energy models and in economic models. A distinction is made between pure processing networks (with conservation of flow and capacity bounds on arcs) and generalized processing networks (conservation of flow in nodes but not necessarily on arcs). The book starts with a survey of network flow programming for pure and generalized networks with an emphasis on the primal simplex algorithm. Primal simplex based methods are then presented for several kinds of processing networks; these algorithms try to exploit as much as possible the special basis structure so that many of the simplex computations can be performed by graph-theoretical techniques. Finally relations between processing networks and general LP models are discussed (including the multicommodity flows). The presentation is generally clear and motivating. It would have been nice to support the discussion of these methods with some convincing computational results. In summary this book will provide an interesting reading to those who want to know more about network programming and its extensions with a view to develop efficient codes.
D. de WERRA Ecole Polytechnique Fbdbrale de Lausanne Lausanne, Switzerland
Roy D. SHAPIRO
Optimisation Models for Planning and Allocation: Text and Cases in Mathematical Programming Wiley, New York, 1985, 650 pages Writers of OR texts face a difficult problem. Should they emphasise the real and successful application of formal models or should they em-
sign with unknown arc-capacities and 'multiterminal channel routing'. Three papers deal with different problems arising in database theory. One of these provides an interesting study of algorithms to detect strong equivalence--a notion based on the concepts of kernels--of hypergraphs. Another paper presents algorithms for relational data-base processing to be used on VLSI mesh-of-tree processor structures. A systematic analysis of parameters of a special tree-datastructure (trie) and various applications are presented in a third paper. Approximate algorithms have become an important means in attacking NP-complete problems. Three papers deal with such algorithms for k-center, weighted vertex, multiple edge cover and dominating set problems, the maximum clique and set packing problem. One interesting result is that in a certain probabilistic environment the dominating set problem can always be solved asymptotically optimally by a randomly selected feasible solution. Among the graph theoretic papers one study contains an elegant characterization of the relations between the consistency of quadratic boolean equations and the K~nig-Egervfiry property. Especially for those who are working on VLSIchip-design the paper on channel routing of multiterminal nets may be of particular interest. It presents a fast algorithm for wiring multiterminal pin nets in at most three layers of a grid-structured channel, allowing connections (' vias') between different layers while guaranteeing a maximum channel width of at most twice the density of the problem. This book may be of value for all who are working on related topics and especially for those interested in algorithmic aspects of combinatorial optimization.
O. HOLLAND University of Bonn Bonn, Germany, Fed. Rep.
J. K O E N E
Minimal Cost Flow in Processing Networks: A Primal Approach CWI Tract 4, Amsterdam, 1983, iv + 157 pages, Dfl.22.70
257
The main issue of this work is a treatment of primal simplex based procedures for solving processing network problems. By processing network the author means a generalized network where a given flow may split up into several components with given proportions (refining process) or several components may be blended with given proportions (blending process). Such structures occur in production planning, in assembly models, in energy models and in economic models. A distinction is made between pure processing networks (with conservation of flow and capacity bounds on arcs) and generalized processing networks (conservation of flow in nodes but not necessarily on arcs). The book starts with a survey of network flow programming for pure and generalized networks with an emphasis on the primal simplex algorithm. Primal simplex based methods are then presented for several kinds of processing networks; these algorithms try to exploit as much as possible the special basis structure so that many of the simplex computations can be performed by graph-theoretical techniques. Finally relations between processing networks and general LP models are discussed (including the multicommodity flows). The presentation is generally clear and motivating. It would have been nice to support the discussion of these methods with some convincing computational results. In summary this book will provide an interesting reading to those who want to know more about network programming and its extensions with a view to develop efficient codes.
D. de WERRA Ecole Polytechnique Fbdbrale de Lausanne Lausanne, Switzerland
Roy D. SHAPIRO
Optimisation Models for Planning and Allocation: Text and Cases in Mathematical Programming Wiley, New York, 1985, 650 pages Writers of OR texts face a difficult problem. Should they emphasise the real and successful application of formal models or should they em-