RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



TMF:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


TMF, 2003, Volume 136, Number 1, Pages 164–176 (Mi tmf209)  

This article is cited in 1 scientific paper (total in 1 paper)

Combinatorial Optimization Problems in Ultrametric Spaces

M. D. Missarov, R. G. Stepanov

Kazan State University

Abstract: We study the solutions of some known combinatorial optimization problems including the minimum matching problem, the minimum spanning tree problem, and the traveling salesman problem in $d$-dimensional $p$-adic spaces. It appears that the greedy algorithms yield the optimal solutions of these problems in the ultrametric space, which allows obtaining explicit expressions for the estimates of their averages. We study the asymptotic behavior of these averages as the number of points increases infinitely and find some similarities to the Euclidean case, as well as new, unexpected properties.

Keywords: traveling salesman problem, minimum matching, ultrametricity, greedy algorithms, renormalization group, $p$-adic spaces, self-averaging property

DOI: https://doi.org/10.4213/tmf209

Full text: PDF file (250 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2003, 136:1, 1037–1047

Bibliographic databases:

Received: 15.05.2002

Citation: M. D. Missarov, R. G. Stepanov, “Combinatorial Optimization Problems in Ultrametric Spaces”, TMF, 136:1 (2003), 164–176; Theoret. and Math. Phys., 136:1 (2003), 1037–1047

Citation in format AMSBIB
\Bibitem{MisSte03}
\by M.~D.~Missarov, R.~G.~Stepanov
\paper Combinatorial Optimization Problems in Ultrametric Spaces
\jour TMF
\yr 2003
\vol 136
\issue 1
\pages 164--176
\mathnet{http://mi.mathnet.ru/tmf209}
\crossref{https://doi.org/10.4213/tmf209}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2025787}
\zmath{https://zbmath.org/?q=an:1178.90294}
\transl
\jour Theoret. and Math. Phys.
\yr 2003
\vol 136
\issue 1
\pages 1037--1047
\crossref{https://doi.org/10.1023/A:1024505824594}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000184767700011}


Linking options:
  • http://mi.mathnet.ru/eng/tmf209
  • https://doi.org/10.4213/tmf209
  • http://mi.mathnet.ru/eng/tmf/v136/i1/p164

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. D. Missarov, “Stepen ultrametrichnosti metricheskogo prostranstva”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 154, no. 4, Izd-vo Kazanskogo un-ta, Kazan, 2012, 139–145  mathnet
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:287
    Full text:127
    References:22
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020