Minmax p-traveling salesmen location problems on a tree

Suppose that p traveling salesmen must visit together all points of a tree, and the objective is to minimize the maximum of the lengths of their tours. The location–allocation version of the problem (where both optimal home locations of the salesmen and their optimal tours must be found) is known to be NP-hard for any p ≥ 2. We present exact polynomial algorithms with a linear order of complexity for location versions of the problem (where only optimal home locations must be found, without the corresponding tours) for the cases p = 2 and p = 3.