Unformatted text preview: T j = ∑ i ∈ A j t i will be the load of machine j . Our goal is to ﬁnd an assignment of jobs to machines that would minimize max j T j . Denote this minimum value OPT . Consider a slightly modiﬁed 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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- Winter '09
- Professor Amin Saberi, minimum value OP, approximation factor