A polynomial-time approximation scheme for the Euclidean problem on a cycle cover of a graph / Khachai M.Y., Neznakhina E.D. // Proceedings of the Steklov Institute of Mathematics. - 2015. - V. 289, l. . - P. 111-125.

ISSN:
00815438
Type:
Article
Abstract:
We study the minimum-weight k-size cycle cover problem (Min-k-SCCP) of finding 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 in the general case and preserves intractability even in the geometric statement. For the metric subclass of the problem, a 2-approximation algorithm is proposed. For the Euclidean Min-2-SCCP, a polynomial-time approximation scheme based on Arora’s approach is built. © 2015, Pleiades Publishing, Ltd.
Author keywords:
cycle cover of size k; NP-hard problem; polynomial-time approximation scheme; traveling salesman problem
Index keywords:
нет данных
DOI:
10.1134/S0081543815050107
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https://www.scopus.com/inward/record.uri?eid=2-s2.0-84932634769&doi=10.1134%2fS0081543815050107&partnerID=40&md5=bfda03846e3d6f035648548268aad97c
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Affiliations Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, Russian Federation; Institute of Mathematics and Computer Science, Ural Federal University, pr. Lenina 51, Yekaterinburg, Russian Federation
Author Keywords cycle cover of size k; NP-hard problem; polynomial-time approximation scheme; traveling salesman problem
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Correspondence Address Khachai, M.Y.; Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Russian Federation
Publisher Maik Nauka-Interperiodica Publishing
Language of Original Document English
Abbreviated Source Title Proc. Steklov Inst. Math.
Source Scopus