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∥Cmax 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 √2-approximation algorithm and prove that there is no polynomial time p-approximation algorithm with p < 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). © Springer-Verlag 2004.
CITATION STYLE
Ageev, A. A., Fishkin, A. V., Kononov, A. V., & Sevastianov, S. V. (2004). Open block scheduling in optical communication networks. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2909, 13–26. https://doi.org/10.1007/978-3-540-24592-6_2
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