Approximating interval scheduling problems with bounded profits

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Abstract

We consider the Generalized Scheduling Within Intervals (GSWI) problem: given a set J of jobs and a set J of intervals, where each job j ∈ J has in interval I ∈ I length (processing time) ℓj,I and profit Pj, I, find the highest-profit feasible schedule. The best approximation ratio known for GSWI is (1/2 - ε). We give a (1 - 1/e - ε)-approximation scheme for GSWI with bounded profits, based on the work by Chuzhoy, Rabani, and Ostrovsky [4] for the {0, l}-profit case. We also consider the Scheduling Within Intervals (SWI) problem, which is a particular case of GSWI where for every j ∈ J there is a unique interval I = Ij ∈ I with Pj,I > 0. We prove that SWI is (weakly) NP-hard even if the stretch factor (the maximum ratio of job's interval size to its processing time) is arbitrarily small, and give a polynomial-time algorithm for bounded profits and stretch factor < 2. © Springer-Verlag Berlin Heidelberg 2007.

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Beniaminy, I., Nutov, Z., & Ovadia, M. (2007). Approximating interval scheduling problems with bounded profits. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4698 LNCS, pp. 487–497). Springer Verlag. https://doi.org/10.1007/978-3-540-75520-3_44

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