Computational Geometric Approach to Submodular Function Minimization for Multiclass Queueing Systems

Authors:
Toshinari Itoko;Satoru Iwata
Affiliations:
Tokyo Research Laboratory, IBM, Japan;Research Institute for Mathematical Sciences, Kyoto University,
Venue:
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Year:
2007

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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(n2) time, where nis the cardinality of the ground set. This is much faster than direct applications of general submodular function minimization algorithms.