Introduction to the Techniques of Combinatorial Optimization
Optimization is concerned with finding the best (or optimal) solution to a problem. In this book we are concerned with problems that can be stated in an unambiguous way, usually in terms of mathematical notation and terminology. It is also assumed that the value of any solution to a given problem can be measured in a quantifiable way and this value can be compared with that of any other solution to the problem. Problems of this nature have been posed since the beginning of mankind One of the earliest is recorded by Virgil in his Aeneid where he relates the dilemma of Queen Dido, who was to be given all the land she could enclose in the hide of a bull. She cut the hide into thin strips and joining these together formed a semicircle within which she enclosed a sizeable portion of land with the Mediterranean coast as the diameter. Later Archimedes conjectured that her mathematical solution was optimal; that is, a semicircle is the curve of fixed length which will, together with a straight line, enclose the largest possible area. This conjecture can be proved using a branch of optimization called the calculus of variations.
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