Chapter 1

An Introduction to Combinatorial Problems and Techniques

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Determining Existence Counting Optimization

algorithm

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1.1 THE TIME TO COMPLETE A PROJECT

The Problem

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Analysis

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The Complete Diagram

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Critical Path Analysis (PERT)

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Critical Path

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A Construction Example

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1.2 AMATCHING PROBLEM The Problem

An airline flying out of New York has seven long flights on its Monday morning schedule: Los Angeles, Seattle, London, Frankfurt, Paris, Madrid, and Dublin. Fortunately, seven capable pilots are available: Alfors, Timmack, Jelinek, Tang, Washington, Rupp, and Ramirez. There is a complication, however. Pilots are allowed to request particular destinations, and these requests are to be honored if possible. The pilots and the cities they requested are as follows: Los Angeles: Timmack, Jelinek, Rupp Seattle: Alfors, Timmack, Tang, Washington London: Timmack, Tang, Washington Frankfurt: Alfors, Tang, Rupp, Ramirez Paris: Jelinek, Washington, Rupp Madrid: Jelinek, Ramirez Dublin: Timmack, Rupp, Ramirez

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Analysis

(1)How much work will this be? In particular, how many arrangements will we have to check?

(2)How can we generate all possible arrangements so that we are sure we have not missed any?

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The Practicality of Our Solution to the Airline Problem

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1.3 A KNAPSACK PROBLEM

The Problem

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1.4 ALGORITHMS AND THEIREFFICIENCY

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