Approximation Algorithms for the Maximum m-Peripatetic Salesman Problem

  • Edward Kh. Gimadi
  • Oxana Yu. TsidulkoEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10716)


We consider the maximum m-Peripatetic Salesman Problem (MAX m-PSP), which is a natural generalization of the classic Traveling Salesman Problem. The problem is strongly NP-hard. In this paper we propose two polynomial approximation algorithms for the MAX m-PSP with different and identical weight functions, correspondingly. We prove that for random inputs uniformly distributed on the interval [ab] these algorithms are asymptotically optimal for \(m=o(n)\). This means that with high probability their relative errors tend to zero as the number n of the vertices of the graph tends to infinity. The results remain true for the distributions of inputs that minorize the uniform distribution.


Maximum m-Peripatetic Salesman Problem Time complexity Edge-disjoint Hamiltonian cycles 



The authors are supported by the Russian Foundation for Basic Research grants 16-31-00389 and 15-01-00976, Russian Ministry of Science and Education under 5-100 Excellence Program, and the grant of Presidium of RAS (program 8, project 227).


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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