Abstract
We study a scheduling problem involving the optimal placement of advertisement images in a shared space over time. The problem is a generalization of the classical scheduling problem P∥C max, and involves scheduling each job on a specified number of parallel machines (not necessarily simultaneously) with a goal of minimizing the makespan. In 1969 Graham showed that processing jobs in decreasing order of size, assigning each to the currently-least-loaded machine, yields a 4/3-approximation for P∥C max. Our main result is a proof that the natural generalization of Graham’s algorithm also yields a 4/3-approximationto the minimum-space advertisement scheduling problem. Previously, this algorithm was only known to give an approximation ratio of 2, and the best known approximation ratio for any algorithm for the minimum-space ad scheduling problem was 3/2. Our proof requires a number of new structural insights, which leads to a new lower bound for the problem and a non-trivial linear programming relaxation. We also provide a pseudo-polynomial approximation scheme for the problem (polynomial in the size of the problem and the number of machines).
This work was supported by NSF contracts CCR-0098018 and ITR-0121495.
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Dean, B.C., Goemans, M.X. (2003). Improved Approximation Algorithms for Minimum-Space Advertisement Scheduling. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds) Automata, Languages and Programming. ICALP 2003. Lecture Notes in Computer Science, vol 2719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45061-0_87
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DOI: https://doi.org/10.1007/3-540-45061-0_87
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