The Chinese deliveryman problem

We introduce the Chinese deliveryman problem where the goal of the deliveryman is to visit every house in his neighborhood such that the average time of arrival is minimized. We show that, in contrast to the well-known Chinese postman problem, the Chinese deliveryman problem is APX-hard in general and NP-hard for planar graphs. We give a simple 2-approximation for undirected graphs and a 4 / 3-approximation for 2-edge connected graphs. We observe that there is a PTAS for planar graphs and that depth first search is optimal for trees