an:05054342
Zbl 1097.68011
Ageev, A. A.; Fishkin, A. V.; Kononov, A. V.; Sevastyanov, S. V.
Open block scheduling in optical communication networks
EN
Theor. Comput. Sci. 361, No. 2-3, 257-274 (2006).
00186064
2006
j
68M10 68M20
scheduling; approximation; open shop; data packets
Summary: 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 \((OB||C_{\max})\) 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 \(\sqrt 2\)-approximation algorithm and prove that there is no polynomial time \(\rho\)-approximation algorithm with \(\rho < 11/10\), unless \(\text{P}=\text{NP}\). For the case when the number of machines is fixed, we show that the problem admits a linear time PTAS. In addition, we show that the two-machine problem with release dates is NP-hard in the strong sense.