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Towards Minimizing k-Submodular Functions

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Combinatorial Optimization (ISCO 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7422))

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Abstract

In this paper we investigate k-submodular functions. This natural family of discrete functions includes submodular and bisubmodular functions as the special cases k = 1 and k = 2 respectively.

In particular we generalize the known Min-Max-Theorem for submodular and bisubmodular functions. This theorem asserts that the minimum of the (bi)submodular function can be found by solving a maximization problem over a (bi)submodular polyhedron. We define a k-submodular polyhedron, prove a Min-Max-Theorem for k-submodular functions, and give a greedy algorithm to construct the vertices of the polyhedron.

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Author information

Authors and Affiliations

  1. School of Engineering and Computing Sciences, Durham University, South Road, Durham, DH1 3LE, UK

    Anna Huber

  2. Institute of Science and Technology Austria, Am Campus 1, 3400, Klosterneuburg, Austria

    Vladimir Kolmogorov

Authors
  1. Anna Huber
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  2. Vladimir Kolmogorov
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Editor information

Editors and Affiliations

  1. LAMSADE, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775, Paris Cedex 16, France

    A. Ridha Mahjoub  & Vangelis Th. Paschos  & 

  2. Department of Informatics, Athens University of Economics and Business, 76 Patission str., 10434, Athens, Greece

    Vangelis Markakis  & Ioannis Milis  & 

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Huber, A., Kolmogorov, V. (2012). Towards Minimizing k-Submodular Functions. In: Mahjoub, A.R., Markakis, V., Milis, I., Paschos, V.T. (eds) Combinatorial Optimization. ISCO 2012. Lecture Notes in Computer Science, vol 7422. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32147-4_40

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  • DOI: https://doi.org/10.1007/978-3-642-32147-4_40

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32146-7

  • Online ISBN: 978-3-642-32147-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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