Open block scheduling in optical communication networks

Authors:
A. A. Ageev;A. V. Fishkin;A. V. Kononov;S. V. Sevastyanov
Affiliations:
Sobolev Institute of Mathematics, Novosibirsk, Russia;Institut für Informatik und Praktische Mathematik, Christian-Albrechts-Universität zu Kiel, Kiel, Germany;Sobolev Institute of Mathematics, Novosibirsk, Russia;Sobolev Institute of Mathematics, Novosibirsk, Russia
Venue:
Theoretical Computer Science - Approximation and online algorithms
Year:
2006

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Abstract

In this paper the process of data transmission in star coupled optical communication networks is modelled as a shop-type scheduling problem, where channels (wavelengths) are treated as machines. We formulate an Open Block problem with the minimum makespan objective (O B||Cmax) 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 simultaneously (in a common block) or, alternatively, at disjoint time intervals. We show that the problem is polynomially solvable for 4 machines, NP-hard for 6 machines and strongly NP-hard for a variable number of machines. 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 ρ-approximation algorithm with ρ