Abstract
We consider the problem of scheduling a set of intervals with controllable processing times in the presence of release dates and deadlines on a set of identical parallel machines in order to maximize either the number (the size problem) or the total weight (the weight problem) of accepted intervals. We call these jobs degradable intervals. We study a special case, called the immediate case, in which each accepted interval has to start at its release date. We call the general case the non-immediate case. For both criteria, we present optimal algorithms for the immediate case. For the non-immediate case, we prove the NP-hardness of the size problem and present a 1.58-approximation algorithm. For the weight problem, we propose a 2.54-approximation algorithm.
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© 2004 Springer-Verlag Berlin Heidelberg
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Baille, F., Bampis, E., Laforest, C. (2004). Maximization of the Size and the Weight of Schedules of Degradable Intervals. In: Chwa, KY., Munro, J.I.J. (eds) Computing and Combinatorics. COCOON 2004. Lecture Notes in Computer Science, vol 3106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27798-9_25
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DOI: https://doi.org/10.1007/978-3-540-27798-9_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22856-1
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