Abstract
This paper presents an efficient algorithm for minimizing a certain class of submodular functions that arise in analysis of multiclass queueing systems. In particular, the algorithm can be used for testing whether a given multiclass M/M/1 achieves an expected performance by an appropriate control policy. With the aid of the topological sweeping method for line arrangement, our algorithm runs in O(n 2) time, where n is the cardinality of the ground set. This is much faster than direct applications of general submodular function minimization algorithms.
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A preliminary version of this paper has appeared in Proceedings of the Twelfth International Conference on Integer Programming and Combinatorial Optimization (2007), LNCS 4513, Springer-Verlag, pp. 267–279.
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Itoko, T., Iwata, S. Computational geometric approach to submodular function minimization for multiclass queueing systems. Japan J. Indust. Appl. Math. 29, 453–468 (2012). https://doi.org/10.1007/s13160-012-0074-0
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DOI: https://doi.org/10.1007/s13160-012-0074-0