an:06007825
Zbl 1249.90296
Ageev, A. A.; Pyatkin, A. V.
A 2-approximation algorithm for the metric 2-peripatetic salesman problem
RU
Diskretn. Anal. Issled. Oper. 16, No. 4, 3-20 (2009).
00295633
2009
j
90C35
approximation algorithm; Hamiltonian cycle; spanning tree; traveling salesman problem
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 \textit{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. \textit{A. E. Baburin, Eh. Kh. Gimadi}, and \textit{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.
Zbl 0309.90059; Zbl 1045.05082