Book Selection paper proves nothing new about these two concepts, but does show they are related. There is little in this text for the operational researcher. ROGER KNOTT Bonn WOrkshop on Combinatorial Optimization A. BACHEM, M. GR~TSCHEL and B. KORTE (EDITORS) North Holland, 1982. 312pp. $55.75, Dfl.l20.00 ISBN 0 444 86366 4

In August 1980 a workshop on combinatorial optimization was held at the Institute of Operations Research at the University of Bonn. This text grew out of the lectures given there and comprises 18 papers on a variety of topics, ranging from submodular functions to perfect graphs. Most of the papers describe recent research results by the authors in various fields of combinatorial optimization. Consequently the articles are very theoretical and abstract, so it is difficult to predict which (if any) will be of long-term significance to the operational research community. Those papers which the reviewer found to have the closest links with operational research are described below. 1.

The Travelling Salesman Polytope and (0.2)-Matchings, by G. Corneujols and W.R. Pulleyblank. This paper describes a theoretical method of verification for proposed optimal solutions to the travelling salesman problem. Although the method can solve problems of matching and branching, it has so far been unable to solve the travelling salesman problem. The partial solutions so far obtained have, in the authors words, "provided the basis for successful cutting plane approaches to real world problems".

2.

Optimal Subtrees and Extensions, by H. Groflin, Th. M. Liebling and A. Predon. This paper considers the problem of finding an optimal family of nested rooted subtrees of a tree. Applications to pipeline networks are considered.

3.

Degree-Two Inequalities, Clique Facets and Biperfect Graphs, by E.L. Johnson and M.W. Padberg. This paper considers ine quality sys tems with zero-one variables where each inequality has only two variables. Such inequalities, it is claimed, arise as logical implications of gene ral zero-one programming problems.

4.

Scheduling Problems with a Singular Solution, by ~H. Mohring. This paper considers the tasks (a) of minimising a regular performance measure subj e ct to res ource constraints and (b) of minimising costs for resource r equirements subject to a fixed completion time for arbitrary project networks with resource requirements. Problems with a singular solution, it is stated, have practical importance as test examples for heuristic algorithms for arbitrary scheduling problems.

Even the papers described above are highly theoretical. The book as a whole is one to borrow rather than buy, unless you are active in the field of combinatorial optimization. IDGER KNOTT

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