Bellman R., Cooke K.L., Lockett J.A. Algorithms Graphs and Computers

Academic Press, 1970. — 252.The development of the electronic computer has profoundly and irrevocably changed the scientific world. In so doing it has simultaneously created numerous opportunities for the application of mathematical ideas and methods to the solution of traditional scientific problems and made possible the exploration of research areas in mathematics and the sciences either previously unattainable or undreamt of. We are, in consequence, living in one of the great times of intellectual history.
Among the most exciting of the new areas of mathematical research and applications are those related to the structure, operation, and control of large systems. Our society is composed of a number of partially interlocking systems, economic, industrial, military, political, educational, and medical. Mathematical problems connected with these systems are thus well worth studying, and indeed are becoming of fundamental importance. The objective of this book is to provide an introduction to these new problems, to some of the mathematical theories and methods employed their analysis, and to the role of the high speed digital computer in their resolution.
The book is thus addressed to readers seeking a first acquaintance with problems of this type, either for a general view of the methodologies solution or for specific information concerning mathematical and computational solution methods. It is also addressed to readers sceking to obtain some ideas of the different uses of computers in problem solving. We expect that most readers will have a previous or concurrent course in the elements of computer programming. However, many such courses aim developing facility with certain specific intricacies of computer programming, rather than an appreciation of the overall power of the computer to aid in the treatment of classes of major problems of science and society.
What we hope to develop particularly is skill in problem analysis. We proceed from the original verbal problem, imprecisely formulated, and deliberately so, through mathematical equations to flow charts. Our point of view is that the solution of a problem must begin with precise formulation and conclude with a feasible computational scheme. However, since programming languages vary widely and change quickly we have not, with one or two exceptions, supplied programs. A number of exercises call for the writing of programs, and we expect that many readers will wish to test their skill with some of these.Commuting and Computing
The Method of Successive Approximations
From Chicago to the Grand Canyon by Car and Computer: Difficulties Associated with Large Maps
Proof of the Validity of the Method
Juggling Jugs
The Sawyer Graph and the Billiard Ball Computer
Cannibals and Missionaries
The “Travelling Salesman” and Other Scheduling Problems