pset4 - EECS 310, Fall 2011 Instructor: Nicole Immorlica...

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EECS 310, Fall 2011 Instructor: Nicole Immorlica Problem Set #4 Due: October 20, 2011 1. (20 points) You have n jobs J = { 1 ,...,n } that must be scheduled on m machines M = { 1 ,...,m } . Each job i can only be processed by a subset M i M of the machines. Furthermore, each machine can process only a total number of k i jobs. Derive a condition similar to that in Hall’s Theorem to determine whether all the jobs can be scheduled. Use Hall’s Theorem to prove that your condition is necessary and suﬃcient. 2. (20 points) A company wishes to interview n candidates for job opening. Each candidate can be interviewed by exactly k managers and, conversely, each manager is qualiﬁed to interview exactly k candidates. As CEO, you must ﬁnd a schedule of interviews such that: each interview takes one hour, each manager interviews at most one candidate per hour, each candidate is interviewed at most once in any given hour, and each candidate is interviewed k times. Prove that there exists a schedule of interviews such that the entire interview process

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This note was uploaded on 01/15/2012 for the course ECON 101 taught by Professor N/a during the Fall '11 term at Middlesex CC.

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pset4 - EECS 310, Fall 2011 Instructor: Nicole Immorlica...

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