Asymptotically optimal algorithms for geometric Max TSP and Max m-PSP

We consider the maximum traveling salesman problem (Max TSP) and the maximum mm-peripatetic salesman problem (Max m-PSP) on assuming that the vertices of a graph lie in some geometric space. For the both problems we obtain approximation algorithms that find asymptotically optimal solutions in the case of a normed space with a bounded dimension and in the case of a polyhedral space with a bounded number of facets, respectively.