Abstract
The Variable Length Scheduling Problem has been studied in the context of web searching, where the execution time for a task depends on the start time for the task. The objective is to minimize the total completion time of all the tasks. It is known that the problem is NP-Hard to approximate within a factor of n O(1). For the case when the execution times are from the set 1, 2, the optimal execution sequence can be determined in polynomial time. Also, when the execution times are from the set k 1, k 2 the problem is NP-complete and can be approximated within a ratio of \( 2 + \tfrac{{k_2 }} {{2k_1 }} \) . Here we note that the approximation ratio for the case when the execution times are from the set k 1, k 2 can be improved to \( 2 + \tfrac{{2k_2 }} {{5k_1 }} \) .
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Gaur, D.R., Krishnamurti, R. (2003). Scheduling Intervals Using Independent Sets in Claw-Free Graphs. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds) Computational Science and Its Applications — ICCSA 2003. ICCSA 2003. Lecture Notes in Computer Science, vol 2667. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44839-X_28
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DOI: https://doi.org/10.1007/3-540-44839-X_28
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