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Linear and combinatorial optimization in ordered algebraic structures
Book Revie.~
118
and circulations. Each chapter has a set of exercises and also additional notes and bibliography. The book is completed by solutions to selected exercises, a main bibliography and subject and author indexes. This is a good introductory text book. Although it has an algebraic "flavour", an adequate mathematical background is provided so that the non-mathematician need not be deterred. The book is self-contained and should be useful to anyone approaching this particular aspect of O.R. whether student or otherwise. The solutions to selected exercises are a nice feature which may make the book particularly useful to those in the "'otherwise'" category. Some important topics (e.g. network location problems) are not covered. Also, the Travelling Salesman Problem, for historical reasons, deserves a somewhat fuller treatment and Branch and Bound methods are inadequatly covered. Nevertheless, the book contains nothing superfluous. On the practical side I would have liked to see more emphasis on storage/execution time requirements of algorithms but applications are illustrated throughout with many interesting examples from various subjects.
C.J. PURSGLO lie University of Liverpool Liuerpool, U~ffted Kingdom U. ZIMMERMANN
Volume 10 in: Annals of Discrete Mathematics, North-Holland, Amsterdam, 1981, ix + 380 pages, Dfl. 125.00 This book is a welcome addition to the literature on Combinatorial Optimisation. Algebraic formulations provide a unifying framework in which related but nevertheless quite distinct problems can be tackled by a single method: e.g. the ordinary assignment problem and the bottleneck as.~,~gnment problem become particular examples of an algebraic assignment problem as follows: al~(i ) + a2~(2 ) +
minimise a i,(l) * a 2 , ( 2 )
* " " " *
an~,(n)
where the a o are the elements of an ordered semigroup with binary operation . . The book is divided into two parts. Part 1 deals with the basic mathematical properties of the ordered algebraic structures that are needed for the methods of Part 2. It is quite long and it might have been better to have dispersed it throughout the book, so that one could get a mixture of methods and theory as one went along. Nevertheless it is a fairly comprehensive and useful set of results. Part 2 covers many of the areas in which the algebraic approach has provided useful results; algebraic path problems, eigenvalue problems, linear programs, slow problems and independent set problems. I particularly enjoyed the chapter on algebraic path problems showing the power of the generalised Gauss-Jordan procedure. The book will be mainly of interest to people doing theoretical research in Combinatorial Optimisation.
A.M. FRIEZE London University London, United Kingdom Moshe BEN-HORIM and Haim LEVY
Linear and Combinatorial Optimization in Ordered Algebraic Structures
minimise
over permutations of { 1, 2 .... n} are special cases of
• • •
+an~,(n)
or
minimise max( a l~(, ), a 2~(2) . . . . an~(.) )
Statistics: Decisions and Applications in Business and F~onomics Random House, New York, 1981, xix + 772 pages The book is in Content and structure almost identical to the second edition of "Basic Statistics for Business and Economics" by Hoel-Jessen. The latter does the same job (plus an additional chapter on Survey Designs) with 250 pages less. Both books are designed for a two-semester course and both avoid mathematics beyond high-school algebra ('though the reader will encounter an occasional integration). What se~s the present book apart from Hoel-Jessen and similar elementary texts for business and economics majors is that it has been written with a student in mind who has a pocket calculator at his disposal and access to a computer with packaged statistical programs. The
118
and circulations. Each chapter has a set of exercises and also additional notes and bibliography. The book is completed by solutions to selected exercises, a main bibliography and subject and author indexes. This is a good introductory text book. Although it has an algebraic "flavour", an adequate mathematical background is provided so that the non-mathematician need not be deterred. The book is self-contained and should be useful to anyone approaching this particular aspect of O.R. whether student or otherwise. The solutions to selected exercises are a nice feature which may make the book particularly useful to those in the "'otherwise'" category. Some important topics (e.g. network location problems) are not covered. Also, the Travelling Salesman Problem, for historical reasons, deserves a somewhat fuller treatment and Branch and Bound methods are inadequatly covered. Nevertheless, the book contains nothing superfluous. On the practical side I would have liked to see more emphasis on storage/execution time requirements of algorithms but applications are illustrated throughout with many interesting examples from various subjects.
C.J. PURSGLO lie University of Liverpool Liuerpool, U~ffted Kingdom U. ZIMMERMANN
Volume 10 in: Annals of Discrete Mathematics, North-Holland, Amsterdam, 1981, ix + 380 pages, Dfl. 125.00 This book is a welcome addition to the literature on Combinatorial Optimisation. Algebraic formulations provide a unifying framework in which related but nevertheless quite distinct problems can be tackled by a single method: e.g. the ordinary assignment problem and the bottleneck as.~,~gnment problem become particular examples of an algebraic assignment problem as follows: al~(i ) + a2~(2 ) +
minimise a i,(l) * a 2 , ( 2 )
* " " " *
an~,(n)
where the a o are the elements of an ordered semigroup with binary operation . . The book is divided into two parts. Part 1 deals with the basic mathematical properties of the ordered algebraic structures that are needed for the methods of Part 2. It is quite long and it might have been better to have dispersed it throughout the book, so that one could get a mixture of methods and theory as one went along. Nevertheless it is a fairly comprehensive and useful set of results. Part 2 covers many of the areas in which the algebraic approach has provided useful results; algebraic path problems, eigenvalue problems, linear programs, slow problems and independent set problems. I particularly enjoyed the chapter on algebraic path problems showing the power of the generalised Gauss-Jordan procedure. The book will be mainly of interest to people doing theoretical research in Combinatorial Optimisation.
A.M. FRIEZE London University London, United Kingdom Moshe BEN-HORIM and Haim LEVY
Linear and Combinatorial Optimization in Ordered Algebraic Structures
minimise
over permutations of { 1, 2 .... n} are special cases of
• • •
+an~,(n)
or
minimise max( a l~(, ), a 2~(2) . . . . an~(.) )
Statistics: Decisions and Applications in Business and F~onomics Random House, New York, 1981, xix + 772 pages The book is in Content and structure almost identical to the second edition of "Basic Statistics for Business and Economics" by Hoel-Jessen. The latter does the same job (plus an additional chapter on Survey Designs) with 250 pages less. Both books are designed for a two-semester course and both avoid mathematics beyond high-school algebra ('though the reader will encounter an occasional integration). What se~s the present book apart from Hoel-Jessen and similar elementary texts for business and economics majors is that it has been written with a student in mind who has a pocket calculator at his disposal and access to a computer with packaged statistical programs. The