Abstract
We consider the classic problem of scheduling a set of n jobs non-preemptively on a single machine. Each job j has non-negative processing time, weight, and deadline, and a feasible schedule needs to be consistent with chain-like precedence constraints. The goal is to compute a feasible schedule that minimizes the sum of penalties of late jobs. Lenstra and Rinnoy Kan [Annals of Disc. Math., 1977] in their seminal work introduced this problem and showed that it is strongly NP-hard, even when all processing times and weights are 1. We study the approximability of the problem and our main result is an O(logk)-approximation algorithm for instances with k distinct job deadlines.
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Efsandiari, H., Hajiaghyi, M., Könemann, J., Mahini, H., Malec, D., Sanità, L. (2015). Approximate Deadline-Scheduling with Precedence Constraints. In: Bansal, N., Finocchi, I. (eds) Algorithms - ESA 2015. Lecture Notes in Computer Science(), vol 9294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48350-3_41
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DOI: https://doi.org/10.1007/978-3-662-48350-3_41
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