Universal algorithms for solving the matrix Bellman equations over semirings

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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Correspondence to G. L. Litvinov.

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

Communicated by A. D. Nola.

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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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Keywords

  • Systolic Array
  • Bellman Equation
  • Closure Operation
  • Weighted Directed Graph
  • Universal Algorithm