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Discrete Convex Functions on Graphs and Their Algorithmic Applications

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Combinatorial Optimization and Graph Algorithms

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Abstract

The present article is an exposition of a theory of discrete convex functions on certain graph structures, developed by the author in recent years. This theory is a spin-off of discrete convex analysis by Murota, and is motivated by combinatorial dualities in multiflow problems and the complexity classification of facility location problems on graphs. We outline the theory and algorithmic applications in combinatorial optimization problems.

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Acknowledgements

The author thanks Yuni Iwamasa for careful reading, Satoru Fujishige for remarks, and Kazuo Murota for numerous comments improving presentation. The work was partially supported by JSPS KAKENHI Grant Numbers 25280004, 26330023, 26280004, 17K00029.

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Authors and Affiliations

  1. Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo, 113-8656, Japan

    Hiroshi Hirai

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  1. Hiroshi Hirai
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Correspondence to Hiroshi Hirai .

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Editors and Affiliations

  1. National Institute of Informatics , Tokyo, Japan

    Takuro Fukunaga

  2. National Institute of Informatics , Tokyo, Japan

    Ken-ichi Kawarabayashi

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Hirai, H. (2017). Discrete Convex Functions on Graphs and Their Algorithmic Applications. In: Fukunaga, T., Kawarabayashi, Ki. (eds) Combinatorial Optimization and Graph Algorithms. Springer, Singapore. https://doi.org/10.1007/978-981-10-6147-9_4

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  • DOI: https://doi.org/10.1007/978-981-10-6147-9_4

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