@article {IOPORT.01347065, author = {Anily, Shoshana and Bramel, Julien and Hertz, Alain}, title = {A $\frac{5}{3}$-approximation algorithm for the clusterd traveling salesman tour and path problems.}, year = {1999}, journal = {Operations Research Letters}, volume = {24}, number = {1-2}, issn = {0167-6377}, pages = {29-35}, publisher = {Elsevier Science Publishers (North-Holland), Amsterdam}, doi = {10.1016/S0167-6377(98)00046-7}, abstract = {Summary: We consider the Ordered Cluster Salesman Problem (OCTSP). In this problem, a vehicle starting and ending at a given depot must visit a set of $n$ points. The points are partitioned into $K$, $K\leq n$, prespecified clusters. The vehicle must first visit the points in cluster 1, then the points in cluster $2,\dots$, and finally the points in cluster $K$ so that the distance traveled is minimized. We present a $\frac 53$-approximation algorithm for this problem which runs in $O(n^3)$ time. We show that our algorithm can also be applied to the path version of the OCTSP: the ordered cluster traveling salesman path problem. Here the (different) starting and ending points of the vehicle may or may not be prespecified. For this problem, our algorithm is also a $\frac 53$-approximation algorithm.}, identifier = {01347065}, }