Trudy Instituta Matematiki i Mekhaniki UrO RAN
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Trudy Inst. Mat. i Mekh. UrO RAN:
Year:
Volume:
Issue:
Page:
Find




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

Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Volume 20, Number 4, Pages 297–311 (Mi timm1135)  
This article is cited in 10 scientific papers (total in 10 papers)

Polynomial-time approximation scheme for a Euclidean problem on a cycle covering of a graph

M. Yu. Khachaiab, E. D. Neznakhinaba

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Yeltsin Ural Federal University
Full-text PDF (313 kB) Citations (10)
References:
PDF
HTML
Abstract: We study the Min-$k$-SCCP problem on a partition of a complete weighted digraph into $k$ vertex-disjoint cycles of minimum total weight. This problem is a natural generalization of the known Traveling salesman problem (TSP) and has a number of applications in operations research and data analysis. We show that the problem is strongly $NP$-hard and preserves intractability even in the geometric statement. For a metric special case of the problem, a new polynomial $2$-approximation algorithm is proposed. For the Euclidean Min-$2$-SCCP, a polynomial-time approximation scheme based on Arora's approach is built.
Keywords: $NP$-hard problem, polynomial-time approximation scheme (PTAS), traveling salesman problem (TSP), cycle covering of size $k$.
Received: 13.08.2014
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2015, Volume 289, Issue 1, Pages 111–125
DOI: https://doi.org/10.1134/S0081543815050107
Bibliographic databases:
Document Type: Article
UDC: 519.16+519.85
Language: Russian
Citation: M. Yu. Khachai, E. D. Neznakhina, “Polynomial-time approximation scheme for a Euclidean problem on a cycle covering of a graph”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 4, 2014, 297–311; Proc. Steklov Inst. Math. (Suppl.), 289, suppl. 1 (2015), 111–125
Citation in format AMSBIB
\Bibitem{KhaNez14}
\by M.~Yu.~Khachai, E.~D.~Neznakhina
\paper Polynomial-time approximation scheme for a~Euclidean problem on a~cycle covering of a~graph
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2014
\vol 20
\issue 4
\pages 297--311
\mathnet{http://mi.mathnet.ru/timm1135}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3275890}
\elib{https://elibrary.ru/item.asp?id=22515155}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2015
\vol 289
\issue , suppl. 1
\pages 111--125
\crossref{https://doi.org/10.1134/S0081543815050107}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000356931500010}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84932634769}
Linking options:
  • https://www.mathnet.ru/eng/timm1135
  • https://www.mathnet.ru/eng/timm/v20/i4/p297
    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Trudy Instituta Matematiki i Mekhaniki UrO RAN
    Statistics & downloads:
    Abstract page:340
    Full-text PDF :111
    References:50
    First page:5
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024