Approximation algorithms for the maximum 2-peripatetic salesman problem

Abstract

Under study is the problem of finding two edge-disjoint Hamiltonian cycles (salesman routes) of maximal total weight in a complete undirected graph. For the case of edge weights from the interval [1, q], a polynomial algorithm is constructed with the guaranteed accuracy estimate \(\frac{{3q + 2}} {{4q + 1}}\). For the case of weights 1 and 2 and two different weight functions corresponding to the two routes, a polynomial algorithm with the accuracy estimate \(\frac{{11\rho - 8}} {{18\rho - 15}}\) is presented, where ρ is the accuracy estimate of an algorithm for solving a similar minimum optimization problem.