Approximating Multi-Criteria Max-TSP

We present randomized approximation algorithms for multi-criteria Max-TSP. For Max-STSP with k > 1 objective functions, we obtain an approximation ratio of $1/k - \eps$ for arbitrarily small $\eps > 0$. For Max-ATSP with k objective functions, we obtain an approximation ratio of $1/(k+1) - \eps$.