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Universal algorithms for solving the matrix Bellman equations over semirings

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Abstract

This paper is a survey on universal algorithms for solving the matrix Bellman equations over semirings and especially tropical and idempotent semirings. However, original algorithms are also presented. Some applications and software implementations are discussed.

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Acknowledgments

The authors are grateful to the anonymous referees for a number of important corrections in the paper.

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Authors and Affiliations

  1. A.A. Kharkevich Institute for Information Transmission Problems, and National Research University Higher School of Economics, Moscow, Russia

    G. L. Litvinov & A. N. Sobolevski

  2. Moscow Center for Continuous Mathematical Education, Moscow, Russia

    A. Ya. Rodionov & S. N. Sergeev

  3. University of Birmingham, School of Mathematics, Edgbaston, B15 2TT, UK

    S. N. Sergeev

Authors
  1. G. L. Litvinov
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  2. A. Ya. Rodionov
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  3. S. N. Sergeev
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  4. A. N. Sobolevski
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Corresponding author

Correspondence to G. L. Litvinov.

Additional information

Communicated by A. D. Nola.

This work is supported by the RFBR-CRNF grant 11-01-93106 and RFBR grant 12-01-00886-a.

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Litvinov, G.L., Rodionov, A.Y., Sergeev, S.N. et al. Universal algorithms for solving the matrix Bellman equations over semirings. Soft Comput 17, 1767–1785 (2013). https://doi.org/10.1007/s00500-013-1027-5

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