Abstract
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.
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Acknowledgements
This research has been supported by the Netherlands Organisation for Scientific Research (NWO) under Grant 639.033.403, by BSIK Grant 03018 (BRICKS: Basic Research in Informatics for Creating the Knowledge Society), and by the Interuniversity Attraction Poles Programme initiated by the Belgian Science Policy Office.
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Ficker, A.M.C., Spieksma, F.C.R., Woeginger, G.J. (2017). Balanced Optimization with Vector Costs. In: Jansen, K., Mastrolilli, M. (eds) Approximation and Online Algorithms. WAOA 2016. Lecture Notes in Computer Science(), vol 10138. Springer, Cham. https://doi.org/10.1007/978-3-319-51741-4_8
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DOI: https://doi.org/10.1007/978-3-319-51741-4_8
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