Abstract
In this paper the process of data transmission in optical communication networks is modeled as a shop-type scheduling problem, where channels (wavelengths) are treated as machines. We formulate an Open Block problem with the minimum makespan objective (an \(OB\Vert C_{\rm max}\) problem) in which a relation of a new type between the operations of each job is introduced: any two operations of a job have identical processing times and may be processed either completely simultaneously (in a common block) or, alternatively, with full diversity in time. We show that the problem is polynomially solvable for 4 machines, binary NP-hard for 6 machines and strongly NP-hard for a variable number of machines. Adding release dates to the two-machine problem also leads to the NP-hardness in strong sense. For the case of a variable number of machines we present a polynomial time \(\sqrt{2}\)-approximation algorithm and prove that there is no polynomial time ρ-approximation algorithm with ρ < 11/10, unless P=NP. For the case when the number of machines is fixed, we show that the problem can be solved by a linear time PTAS and by a few linear time statistically optimal algorithms (generating optimal schedules for almost all instances).
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Ageev, A.A., Fishkin, A.V., Kononov, A.V., Sevastianov, S.V. (2004). Open Block Scheduling in Optical Communication Networks. In: Solis-Oba, R., Jansen, K. (eds) Approximation and Online Algorithms. WAOA 2003. Lecture Notes in Computer Science, vol 2909. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24592-6_2
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DOI: https://doi.org/10.1007/978-3-540-24592-6_2
Publisher Name: Springer, Berlin, Heidelberg
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