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Unformatted text preview: T j = i A j t i will be the load of machine j . Our goal is to nd an assignment of jobs to machines that would minimize max j T j . Denote this minimum value OPT . Consider a slightly modied greedy approach to the one showed in class. First, we sort the jobs so that t 1 t 2 t n . Then, we assign them iteratively to the machines, every time to the machine with the smallest load. Show that the approximation factor of this algorithm is at most 3 / 2. Hint: Note that if n > m then t m +1 OPT/ 2. Why is this true? Extra Credit: Prove that the approximation factor of the algorithm is actually equal to 4 / 3....
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This document was uploaded on 06/17/2010.
- Winter '09