Probabilistic analysis of one routing problem

We consider the unit-demand Euclidean vehicle routing problem (VRP), where $n$ customers are modeled as independent identically distributed points on the plane and have unit demand. The Iterated Tour Partitioning heuristic (ITP) for VRP is known. The ITP heuristic is a $2$-approximation algorithm in a general case. But if customers are modeled as i.i.d. points with uniform distribution on the unit square, then it is shown that ITP is a $(2-c)$-approximation algorithm ($c>0$). In the paper, the same result is proved in the case when customers are i.i.d. points with uniform distribution on the circle of the unit area. Ill. 3, bibliogr. 7.