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Submodular Function Maximization on the Bounded Integer Lattice

  • Corinna GottschalkEmail author
  • Britta Peis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9499)

Abstract

We consider the problem of maximizing a submodular function on the bounded integer lattice. As a direct generalization of submodular set functions, \(f: \{0, \ldots , C\}^n \rightarrow \mathbb {R}_+\) is submodular, if \(f(x) + f(y) \ge f(x \wedge y) + f(x \vee y)\) for all \(x,y \in \{0, \ldots , C\}^n\) where \(\wedge \) and \(\vee \) denote element-wise minimum and maximum. The objective is finding a vector x maximizing f(x). In this paper, we present a deterministic \(\frac{1}{3}\)-approximation using a framework inspired by [2]. We also provide an example that shows the analysis is tight and yields additional insight into the possibilities of modifying the algorithm. Moreover, we examine some structural differences to maximization of submodular set functions which make our problem harder to solve.

Notes

Acknowledgement

We thank S.Thomas McCormick and Kazuo Murota for fruitful discussions.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.School of Business and EconomicsRWTH Aachen UniversityAachenGermany

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