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Teoreticheskaya i Matematicheskaya Fizika, 2003, Volume 136, Number 1, Pages 164–176
DOI: https://doi.org/10.4213/tmf209 (Mi tmf209) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Combinatorial Optimization Problems in Ultrametric Spaces

M. D. Missarov, R. G. Stepanov

Kazan State University
Full-text PDF (250 kB) Citations (3)
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DOI: https://doi.org/10.4213/tmf209
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.
Received: 15.05.2002
English version:
Theoretical and Mathematical Physics, 2003, Volume 136, Issue 1, Pages 1037–1047
DOI: https://doi.org/10.1023/A:1024505824594
Bibliographic databases:
Language: Russian
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
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\jour Theoret. and Math. Phys.
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\pages 1037--1047
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  • https://www.mathnet.ru/eng/tmf/v136/i1/p164
    • 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
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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