| Integer Programming and Combinatorics (2008) | |||||||||||||
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| Integer programming and combinatorics are closely linked. In the broadest sense their domains are identical, though in practice some problems are popularly viewed to fall more in the province of one than the other. "Combinatorics," as spoken of here, is the field of "combinatorial optimiza-tion, " whose prcblems characteristically have the form of seeking a "best " subset of items (decisions, activities, etc.) satisfying particular criteria from a structured finite set of alternatives. "Best " is evaluated in terms of maximizing or minimizing some functional. The structure of the finite set, whatever it may be, is the feature to be exploited in devising a systematic method to solve the problem, rather than simply enumerating and comparing all alternatives (which in problems of real world significance can require astronomical amounts of computation). A remarkable number of practical problems fall | |||||||||||||
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