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Submodular systems and related topics

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Mathematical Programming at Oberwolfach II

Part of the book series: Mathematical Programming Studies ((MATHPROGRAMM,volume 22))

Abstract

Let

be a distributive lattice formed by subsets of a finite set with set union and intersection as the lattice operations, and let f be a submodular function on

. The pair (

, f) is called a submodular system and is a generalization of a (poly-)matroid. The present paper makes a survey of the author’s earlier work on submodular systems and provides a unifying view and some useful observations on related topics such as geometries on posets, generalized polymatroids, boundary hypermatroids, submodular functions on crossing families, submodular flows, strongly connected orientations of graphs, Lovász’s extension of set functions, minimization of submodular functions etc. We also show a new approach to the problem of minimizing submodular functions.

Written while the author was at Institut für ökonometrie und Operations Research, Universität Bonn, West Germany.

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Authors and Affiliations

  1. Institute of Socio-Economic Planning, University of Tsukuba, 305, Sakura, Ibaraki, Japan

    Satoru Fujishige

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  1. Satoru Fujishige
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Bernhard Korte Klaus Ritter

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© 1984 The Mathematical Programming Society, Inc.

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Fujishige, S. (1984). Submodular systems and related topics. In: Korte, B., Ritter, K. (eds) Mathematical Programming at Oberwolfach II. Mathematical Programming Studies, vol 22. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0121012

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  • DOI: https://doi.org/10.1007/BFb0121012

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  • Print ISBN: 978-3-642-00914-3

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