Abstract
We study an on-line problem of scheduling parallel jobs on 2-dimensional meshes. Parallel jobs arrive dynamically according to the dependencies between them, which are unknown before the jobs appear. Each job may need more than one processor simultaneously and is required to be scheduled on a submesh of the processors which are located on a 2-dimensional mesh, i.e., a job must be scheduled on a rectangle of given dimensions. The objective is to minimize the maximum completion time (makespan). We deal with an UET job system, in which all job processing times are equal. We show a lower bound of 3.859 and present a 5.25-competitive algorithm. It significantly improves a previous lower bound of 3.25 and a previous upper bound of 46/7. We consider also the rotated 2-dimensional mesh, in which the parallel jobs can be rotated. A lower bound of 3.535 is proven and an on-line algorithm with competitive ratio of at most 4.25 is derived.
Supported by EU-Project CRESCCO (IST-2001-33135) and NSFC (10231060).
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Ye, D., Zhang, G. (2003). Online Scheduling of Parallel Jobs with Dependencies on 2-Dimensional Meshes . In: Ibaraki, T., Katoh, N., Ono, H. (eds) Algorithms and Computation. ISAAC 2003. Lecture Notes in Computer Science, vol 2906. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24587-2_35
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DOI: https://doi.org/10.1007/978-3-540-24587-2_35
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