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On Minimizing Supermodular Functions on Hereditary Systems

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Optimization Problems and Their Applications (OPTA 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 871))

Abstract

The problem of minimizing a supermodular set function is considered. A special case of this problem is the well-known NP-hard minimization p-median problem. The main results of the paper are tight a priori and a posteriori bounds on worst-case behaviour of a “reverse” greedy (steepest descent) algorithm of minimizing a supermodular set function on comatroid. As a corollary, approximation guarantees of this algorithm for the general minimization p-median problem improving the known bounds are obtained.

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Acknowledgements

The research of the first author was supported by the RSF grant 17-11-01117.

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Authors and Affiliations

  1. Omsk State Technical University, Omsk, Russia

    Victor Il’ev

  2. Dostoevsky Omsk State University, Omsk, Russia

    Victor Il’ev & Svetlana Il’eva

Authors
  1. Victor Il’ev
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  2. Svetlana Il’eva
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Corresponding author

Correspondence to Victor Il’ev .

Editor information

Editors and Affiliations

  1. Sobolev Institute of Mathematics SB RAS, Omsk, Russia

    Anton Eremeev

  2. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  3. Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russia

    Yury Kochetov

  4. Industrial and Systems Engineering, University of Florida, Gainesville, Florida, USA

    Panos Pardalos

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Il’ev, V., Il’eva, S. (2018). On Minimizing Supermodular Functions on Hereditary Systems. In: Eremeev, A., Khachay, M., Kochetov, Y., Pardalos, P. (eds) Optimization Problems and Their Applications. OPTA 2018. Communications in Computer and Information Science, vol 871. Springer, Cham. https://doi.org/10.1007/978-3-319-93800-4_1

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  • DOI: https://doi.org/10.1007/978-3-319-93800-4_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-93799-1

  • Online ISBN: 978-3-319-93800-4

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