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Maximization of submodular functions: Theory and enumeration algorithms

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  • Goldengorin, Boris

Abstract

Submodular functions are powerful tools to model and solve either to optimality or approximately many operational research problems including problems defined on graphs. After reviewing some long-standing theoretical results about the structure of local and global maxima of submodular functions, Cherenin's selection rules and his Dichotomy Algorithm, we revise the above mentioned theory and show that our revision is useful for creating new non-binary branching algorithms and finding either approximation solutions with guaranteed accuracy or exact ones.

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  • Goldengorin, Boris, 2009. "Maximization of submodular functions: Theory and enumeration algorithms," European Journal of Operational Research, Elsevier, vol. 198(1), pages 102-112, October.
    • Handle: RePEc:eee:ejores:v:198:y:2009:i:1:p:102-112
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    6. Ivan Contreras & Elena Fernández, 2014. "Hub Location as the Minimization of a Supermodular Set Function," Operations Research, INFORMS, vol. 62(3), pages 557-570, June.
    7. Zhenning Zhang & Donglei Du & Yanjun Jiang & Chenchen Wu, 2021. "Maximizing DR-submodular+supermodular functions on the integer lattice subject to a cardinality constraint," Journal of Global Optimization, Springer, vol. 80(3), pages 595-616, July.
    8. Francisco Casas & Claudio E. Torres & Ignacio Araya, 2022. "A heuristic search based on diversity for solving combinatorial problems," Journal of Heuristics, Springer, vol. 28(3), pages 287-328, June.

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