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A 2-approximation algorithm for the metric 2-peripatetic salesman problem. (Russian) Zbl 1249.90296
Summary: In the $$m$$-peripatetic traveling salesman problem ($$m$$-PSP), given an $$n$$-vertex complete undirected edge-weighted graph, it is required to find $$m$$ edge disjoint Hamiltonian cycles of minimum total weight. The problem was introduced by J. Krarup [Comb. Program.: Methods Appl., Proc. NATO adv. Stud. Inst., Versailles 1974, 173–178 (1975; Zbl 0309.90059)] and has network design and scheduling applications. It is known that the 2-PSP is NP-hard even in the metric case and does not admit any constant-factor approximation in the general case. A. E. Baburin, Eh. Kh. Gimadi, and N. M. Korkishko [Diskretn. Anal. Issled. Oper., Ser. 2 11, No. 1, 11–25 (2004; Zbl 1045.05082)] designed a $$(9/4+\varepsilon)$$-approximation algorithm for the metric case of the 2-PSP, based on solving the traveling salesman problem. We present an improved 2-approximation algorithm with running time $$O(n^2 \log n)$$ for the metric 2-PSP. Our algorithm exploits the fact that the problem of finding two edge disjoint spanning trees of minimum total weight is polynomially solvable.

##### MSC:
 90C35 Programming involving graphs or networks