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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Volume 20, Number 4, Pages 297–311 (Mi timm1135)  
This article is cited in 11 scientific papers (total in 11 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 (11)
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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
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\by M.~Yu.~Khachai, E.~D.~Neznakhina
\paper Polynomial-time approximation scheme for a~Euclidean problem on a~cycle covering of a~graph
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\yr 2014
\vol 20
\issue 4
\pages 297--311
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\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2015
\vol 289
\issue , suppl. 1
\pages 111--125
\crossref{https://doi.org/10.1134/S0081543815050107}
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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