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Revisiting k-sum optimization

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Abstract

In this paper, we address continuous, integer and combinatorial k-sum optimization problems. We analyze different formulations of this problem that allow to solve it through the minimization of a relatively small number of minisum optimization problems. This approach provides a general tool for solving a variety of k-sum optimization problems and at the same time, improves the complexity bounds of many ad-hoc algorithms previously reported in the literature for particular versions of this problem. Moreover, the results developed for k-sum optimization have been extended to the more general case of the convex ordered median problem, improving upon existing solution approaches.

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Acknowledgements

This research has been partially supported by Spanish Ministry of Education and Science/FEDER Grants Numbers MTM2013-46962-C02-(01-02), MTM2016-74983-C2-(1,2)-R, Junta de Andalucía Grant Number FQM 05849 and Fundación Séneca, Grant Number 08716/PI/08.

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Authors and Affiliations

  1. Instituto de Investigacion Matematica de la Universidad de Sevilla (IMUS), Universidad de Sevilla, Seville, Spain

    J. Puerto

  2. Facultad de Ciencias, Universidad de Cádiz, Cádiz, Spain

    A. M. Rodríguez-Chía

  3. School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel

    A. Tamir

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  1. J. Puerto
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  2. A. M. Rodríguez-Chía
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  3. A. Tamir
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Correspondence to J. Puerto.

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Puerto, J., Rodríguez-Chía, A.M. & Tamir, A. Revisiting k-sum optimization. Math. Program. 165, 579–604 (2017). https://doi.org/10.1007/s10107-016-1096-1

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