New approximations for monotone submodular maximization with knapsack constraint

Hongmin W. Du (), Xiang Li () and Guanghua Wang ()
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Hongmin W. Du: Rutgers University
Xiang Li: Santa Clara University
Guanghua Wang: University of Texas at Dallas

Journal of Combinatorial Optimization, 2024, vol. 48, issue 4, No 1, 7 pages

Abstract: 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.

Keywords: Approximation algorithm; Submodular maximization; Knapsack (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10878-024-01214-x

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