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On maximizing monotone or non-monotone k-submodular functions with the intersection of knapsack and matroid constraints

Author

Listed:
  • Kemin Yu

    (Shandong Normal University)

  • Min Li

    (Shandong Normal University)

  • Yang Zhou

    (Shandong Normal University)

  • Qian Liu

    (Shandong Normal University)

Abstract

A k-submodular function is a generalization of a submodular function. The definition domain of a k-submodular function is a collection of k-disjoint subsets instead of simple subsets of ground set. In this paper, we consider the maximization of a k-submodular function with the intersection of a knapsack and m matroid constraints. When the k-submodular function is monotone, we use a special analytical method to get an approximation ratio $$\frac{1}{m+2}(1-e^{-(m+2)})$$ 1 m + 2 ( 1 - e - ( m + 2 ) ) for a nested greedy and local search algorithm. For non-monotone case, we can obtain an approximate ratio $$\frac{1}{m+3}(1-e^{-(m+3)})$$ 1 m + 3 ( 1 - e - ( m + 3 ) ) .

Suggested Citation

  • Kemin Yu & Min Li & Yang Zhou & Qian Liu, 2023. "On maximizing monotone or non-monotone k-submodular functions with the intersection of knapsack and matroid constraints," Journal of Combinatorial Optimization, Springer, vol. 45(3), pages 1-21, April.
    • Handle: RePEc:spr:jcomop:v:45:y:2023:i:3:d:10.1007_s10878-023-01021-w
    DOI: 10.1007/s10878-023-01021-w
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    References listed on IDEAS

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    1. Fisher, M.L. & Nemhauser, G.L. & Wolsey, L.A., 1978. "An analysis of approximations for maximizing submodular set functions - 1," LIDAM Reprints CORE 334, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Zhenning Zhang & Bin Liu & Yishui Wang & Dachuan Xu & Dongmei Zhang, 2022. "Maximizing a monotone non-submodular function under a knapsack constraint," Journal of Combinatorial Optimization, Springer, vol. 43(5), pages 1125-1148, July.
    3. Zhicheng Liu & Longkun Guo & Donglei Du & Dachuan Xu & Xiaoyan Zhang, 2022. "Maximization problems of balancing submodular relevance and supermodular diversity," Journal of Global Optimization, Springer, vol. 82(1), pages 179-194, January.
    4. Fisher, M.L. & Nemhauser, G.L. & Wolsey, L.A., 1978. "An analysis of approximations for maximizing submodular set functions," LIDAM Reprints CORE 341, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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