Approximation Algorithms for \(\alpha\)-bisubmodular Function Maximization Subject to Matroid Constraint

We design an approximation algorithm for maximizing \(\alpha\)-bisubmodular function with matroid constraint, where the \(\alpha\)-bisubmodular function is a generalization of a bisubmodular function. The concept of \(\alpha\)- bisubmodularity is provided by Huber, Krokhin, and Powell [[1], 2014], r...

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Bibliographic Details
Published inJournal of Advances in Mathematics and Computer Science Vol. 38; no. 3; pp. 42 - 48
Main Author Wang, Wenqi
Format Journal Article
LanguageEnglish
Published Journal of Advances in Mathematics and Computer Science 21.02.2023
Subjects
Mathematics
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Summary:We design an approximation algorithm for maximizing \(\alpha\)-bisubmodular function with matroid constraint, where the \(\alpha\)-bisubmodular function is a generalization of a bisubmodular function. The concept of \(\alpha\)- bisubmodularity is provided by Huber, Krokhin, and Powell [[1], 2014], rank function of delta-matroids and the cut capacity of directed networks have \(\alpha\)-bisubmodularity. We consider the two cases of the problem, monotone and non-monotone objective function, respectively. We also show that the running time ispolynomial.
ISSN:2456-9968
2456-9968
DOI:10.9734/jamcs/2023/v38i31750