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We study the preemptive scheduling problem of a set of n jobs with release times and equal processing times on a single machine. The objective is to minimize the sum of the weighted completion times $${\sum_{i=1}^{n}w_{i}C_{i}}$$ of the jobs. We propose for this problem the first parameterized algorithm on the number k of different weights. The runtime of the proposed algorithm is $${O\left(\left(\frac{n}{k}+1\right)^{k}n^{8}\right)}$$ and hence, the problem is polynomially solvable for any fixed number k of different weights.
Mathematics in Computer Science – Springer Journals
Published: Nov 27, 2009
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