An instance of a balanced optimization problem with vector costs consists of a ground set X, a vector cost for every element of X, and a system of feasible subsets over X. The goal is to find a feasible subset that minimizes the spread (or imbalance) of values in every coordinate of the underlying vector costs. We investigate the complexity and approximability of balanced optimization problems in a fairly general setting. We identify a large family of problems that admit a 2-approximation in polynomial time, and we show that for many problems in this family this approximation factor 2 is best-possible (unless P=NP). Special attention is paid to the balanced assignment problem with vector costs, which is shown to be NP-hard even in the highly restricted case of sum costs.
CITATION STYLE
Ficker, A. M. C., Spieksma, F. C. R., & Woeginger, G. J. (2017). Balanced optimization with vector costs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10138 LNCS, pp. 92–102). Springer Verlag. https://doi.org/10.1007/978-3-319-51741-4_8
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