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Combinatorial approximation algorithms for the submodular multicut problem in trees with submodular penalties

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  • Xiaofei Liu

    (Peking University)

  • Weidong Li

    (Yunnan University)

Abstract

In this paper, we introduce the submodular multicut problem in trees with submodular penalties, which generalizes the prize-collecting multicut problem in trees and the submodular vertex cover with submodular penalties. We present a combinatorial approximation algorithm, based on the primal-dual algorithm for the submodular set cover problem. In addition, we present a combinatorial 3-approximation algorithm for a special case where the edge cost is a modular function, based on the primal-dual scheme for the multicut problem in trees.

Suggested Citation

  • Xiaofei Liu & Weidong Li, 0. "Combinatorial approximation algorithms for the submodular multicut problem in trees with submodular penalties," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-13.
    • Handle: RePEc:spr:jcomop:v::y::i::d:10.1007_s10878-020-00568-2
    DOI: 10.1007/s10878-020-00568-2
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    References listed on IDEAS

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    1. Hong Liu & Peng Zhang, 2014. "On the generalized multiway cut in trees problem," Journal of Combinatorial Optimization, Springer, vol. 27(1), pages 65-77, January.
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    Cited by:

    1. Xiaofei Liu & Peiyin Xing & Weidong Li, 2020. "Approximation Algorithms for the Submodular Load Balancing with Submodular Penalties," Mathematics, MDPI, vol. 8(10), pages 1-12, October.
    2. Xiaofei Liu & Weidong Li & Yaoyu Zhu, 2021. "Single Machine Vector Scheduling with General Penalties," Mathematics, MDPI, vol. 9(16), pages 1-16, August.

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    1. Xiaofei Liu & Weidong Li, 2022. "Combinatorial approximation algorithms for the submodular multicut problem in trees with submodular penalties," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1964-1976, October.

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