Submodular Function Maximization on the Bounded Integer Lattice

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9499)


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.


Submodular Function Integer Lattice Submodular Maximization Discrete Convex Analysis Tight Example 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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


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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.School of Business and EconomicsRWTH Aachen UniversityAachenGermany

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