A -approximation algorithm for the clustered traveling salesman tour and path problems (original) (raw)

We consider the Ordered Cluster Traveling 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 n, prespeci ed clusters. The vehicle must rst visit the points in cluster 1, then the points in cluster 2, : : : , and nally the points in cluster K so that the distance traveled is minimized. We present a 5 3-approximation algorithm for this problem which runs in On 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 OCTSPP. Here the di erent starting and ending points of the vehicle may o r m a y not be prespeci ed. For this problem, our algorithm is also a 5 3-approximation algorithm.