lecture 10(1)

# lecture 10(1) - Lecture 10: Classically Hard Decision...

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Lecture 10: Classically Hard Decision Problems Daniel Frances c ± 2012 Contents 1 Two Classical Diﬃcult Problems 2 1.1 The Knapsack Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.1 0-1 Knapsack Problem . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.2 Bounded Knapsack Problem . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.3 Unbounded Knapsack Problem . . . . . . . . . . . . . . . . . . . . . 3 1.1.4 The Subset Sum Problem . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 The Traveling Salesman Problem . . . . . . . . . . . . . . . . . . . . . . . . 3 1

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1 Two Classical Diﬃcult Problems Most of the problems covered in traditional under-graduate OR courses deal with problems for which there either exist polynomial time algorithms, or there is signiﬁcant computational success. For example we have shown that the simplex algorithm is not a polynomial algo- rithm, vast computational experience renders this algorithm of great practical value. Given experience to date it far outweighs the value of the polynomial interior-point method which is generally inferior, except in some isolated large LP problem instances. For Integer Programming problems while there is no existing polynomial time algorithm, many problems of reasonable size, and some very large ones can be solved with existing exponential time algorithms.
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## This note was uploaded on 03/31/2012 for the course MIE 335 taught by Professor Frances during the Spring '12 term at University of Toronto.

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lecture 10(1) - Lecture 10: Classically Hard Decision...

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