Work

New approximations for monotone submodular maximization with knapsack constraint

Year: 2024

Type: article

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.

Source: Journal of Combinatorial Optimization

DOI: 10.1007/s10878-024-01214-x

Authors: Hongmin W. Du, Xiang Li, Guanghua Wang

Institutions: Rutgers, The State University of New Jersey, Santa Clara University, The University of Texas at Dallas

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Santa Clara University, Directorate for Computer and Information Science and Engineering