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H1-ie514 - classified as “conflicting pair” if some...

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IE 514 HOMEWORK #1 DUE: February 16, 2010 Ground Rules: There should be no cooperation within classmates whatsoever. Feel free to ask me or use any books with proper referencing. Yes I know the odd-numbered questions have answers available on the web and I won’t grade them, but try doing them without looking at the answers first. It is always fun to come up with a different model or proof. Question 1: (Murty) Consider the following scheduling problem at an international conference. There are n seminars, {1,2,…,n} planned for this conference. The attendees have been polled and asked to indicate which seminars they plan to attend. Based on the responses, a pair of seminars is
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Unformatted text preview: classified as “conflicting pair” if some attendees want to visit both of them. Let C = {{ a i , b i }: i=1, …, m} be the set of m conflicting pairs classified by the attendees. Each seminar takes the same amount of time. Two seminars can be held in parallel in the same time slot if and only if they do not form a conflicting pair. Subject to this constraint it is required to arrange the seminars using as many parallel sessions as possible at any point of time, so as to keep the conference as short as possible. Design a network model for this problem. Questions 2-7: Chapter 1 (AMO) : 2, 4, 6, 7, 8, 10...
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