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Algebra i Analiz, 2016, Volume 28, Issue 6, Pages 1–19 (Mi aa1512)  

This article is cited in 3 scientific papers (total in 3 papers)

Research Papers

New algorithms for solving tropical linear systems

A. Davydow
Full-text PDF (232 kB) Citations (3)
References:
Abstract: The problem of solving tropical linear systems, a natural problem of tropical mathematics, has already proved to be very interesting from the algorithmic point of view: it is known to be in $NP\cap coNP$, but no polynomial time algorithm is known, although counterexamples for existing pseudopolynomial algorithms are (and must be) very complex.
In this work, the study of algorithms for solving tropical linear systems is continued. First, a new reformulation of Grigoriev's algorithm is presented, which brings it closer to the algorithm of Akian, Gaubert, and Guterman; this makes it possible to formulate a whole family of new algorithms, and, for some algorithms in this family, none of the known superpolynomial counterexamples work. Second, a family of algorithms for solving overdetermined tropical systems is presented.
Also, an explicit algorithm is exhibited that can solve a tropical linear system determined by an $(m\times n)$-matrix with maximal element $M$ in time $\Theta\left(\binom mn\mathrm{poly}\left(m,n,\log M\right)\right)$, and this time matches the complexity of the best of previously known algorithms for feasibility testing.
Keywords: tropical linear system, feasibility, Grigoriev's algorithm, Akian–Gaubert–Guterman algorithm.
Received: 03.06.2016
English version:
St. Petersburg Mathematical Journal, 2017, Volume 28, Issue 6, Pages 727–740
DOI: https://doi.org/10.1090/spmj/1470
Bibliographic databases:
Document Type: Article
Language: English
Citation: A. Davydow, “New algorithms for solving tropical linear systems”, Algebra i Analiz, 28:6 (2016), 1–19; St. Petersburg Math. J., 28:6 (2017), 727–740
Citation in format AMSBIB
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\by A.~Davydow
\paper New algorithms for solving tropical linear systems
\jour Algebra i Analiz
\yr 2016
\vol 28
\issue 6
\pages 1--19
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\transl
\jour St. Petersburg Math. J.
\yr 2017
\vol 28
\issue 6
\pages 727--740
\crossref{https://doi.org/10.1090/spmj/1470}
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  • https://www.mathnet.ru/eng/aa/v28/i6/p1
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Алгебра и анализ St. Petersburg Mathematical Journal
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    Abstract page:210
    Full-text PDF :45
    References:29
    First page:9
     
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