Polynomial Time Approximation Scheme for the Minimum-weight k-Size Cycle Cover Problem in Euclidean space of an arbitrary fixed dimension / Khachay M., Neznakhina K. // IFAC-PapersOnLine. - 2016. - V. 49, l. 12. - P. 6-10.

ISSN:
24058963
Type:
Article
Abstract:
We study the Min-k-SCCP on the partition of a complete weighted digraph by k vertex-disjoint cycles of minimum total weight. This problem is the generalization of the well-known traveling salesman problem (TSP) and the special case of the classical vehicle routing problem (VRP). It is known that the problem Min-k-SCCP is strongly NP-hard and remains intractable even in the geometric statement. For the Euclidean Min-k-SCCP in Rd, we construct a polynomial-time approximation scheme, which generalizes the approach proposed earlier for the planar Min-2-SCCP. For any fixed c > 1, the scheme finds a (1 + 1/c)-approximate solution in time of O(nd+1(k log n)(O (√dc))d-1 2k). © 2016
Author keywords:
cycle cover of size k; NP-hard problem; polynomial-time approximation scheme (PTAS); traveling salesman problem (TSP)
Index keywords:
Approximation theory; Computational complexity; Polynomial approximation; Polynomials; Vehicle routing; Approximate solution; Cycle covers; Minimum total weights; Polynomial time approximation schemes
DOI:
10.1016/j.ifacol.2016.07.541
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https://www.scopus.com/inward/record.uri?eid=2-s2.0-84992374825&doi=10.1016%2fj.ifacol.2016.07.541&partnerID=40&md5=067a815a89d32fac6fb997fe0d3fdb05
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Link https://www.scopus.com/inward/record.uri?eid=2-s2.0-84992374825&doi=10.1016%2fj.ifacol.2016.07.541&partnerID=40&md5=067a815a89d32fac6fb997fe0d3fdb05
Affiliations Krasovsky Institute of Mathematics and Mechanics, Ural Federal University, 16 S.Kovalevskoy str., Ekaterinburg, Russian Federation; Omsk State Technical University, 11 Mira ave., Omsk, Russian Federation
Author Keywords cycle cover of size k; NP-hard problem; polynomial-time approximation scheme (PTAS); traveling salesman problem (TSP)
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Publisher Elsevier B.V.
Language of Original Document English
Abbreviated Source Title IFAC-PapersOnLine
Source Scopus