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New approximations for monotone submodular maximization with knapsack constraint

Author

Listed:
  • Hongmin W. Du

    (Rutgers University)

  • Xiang Li

    (Santa Clara University)

  • Guanghua Wang

    (University of Texas at Dallas)

Abstract

Given a monotone submodular set function with a knapsack constraint, its maximization problem has two types of approximation algorithms with running time $$O(n^2)$$ O ( n 2 ) and $$O(n^5)$$ O ( n 5 ) , respectively. With running time $$O(n^5)$$ O ( n 5 ) , the best performance ratio is $$1-1/e$$ 1 - 1 / e . With running time $$O(n^2)$$ O ( n 2 ) , the well-known performance ratio is $$(1-1/e)/2$$ ( 1 - 1 / e ) / 2 and an improved one is claimed to be $$(1-1/e^2)/2$$ ( 1 - 1 / e 2 ) / 2 recently. In this paper, we design an algorithm with running $$O(n^2)$$ O ( n 2 ) and performance ratio $$1-1/e^{2/3}$$ 1 - 1 / e 2 / 3 , and an algorithm with running time $$O(n^3)$$ O ( n 3 ) and performance ratio 1/2.

Suggested Citation

  • Hongmin W. Du & Xiang Li & Guanghua Wang, 2024. "New approximations for monotone submodular maximization with knapsack constraint," Journal of Combinatorial Optimization, Springer, vol. 48(4), pages 1-7, November.
    • Handle: RePEc:spr:jcomop:v:48:y:2024:i:4:d:10.1007_s10878-024-01214-x
    DOI: 10.1007/s10878-024-01214-x
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    1. Jianxiong Guo & Weili Wu, 2019. "Viral Marketing for Complementary Products," Springer Optimization and Its Applications, in: Ding-Zhu Du & Panos M. Pardalos & Zhao Zhang (ed.), Nonlinear Combinatorial Optimization, pages 309-315, Springer.
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