Point Formation on a line: Contraction Functions and Weber point

In (Sch03), we introduced the concept of Contraction Functions and Contraction Points to solve the point formation problem. We derived several interesting properties and showed that the Weber point is a con- traction point. It is an open question, whether there are contraction points besides the Weber point. Here we modify the problem to point formation on a line. We show that in this case, the Weber point is a possible contraction point, but there are other contraction points as well. In contrast to the Weber point, these other points can be computed eciently.