Fair distribution of bundles

In this paper, we study the problem of splitting fairly bundles of items. We show that given n bundles with m kinds of items in them, it is possible to distribute the value of each kind of item fairly among r persons by breaking apart at most (r-1)m bundles. Moreover, we can guarantee that each participant will receive roughly n/r - mr/2 full bundles. The proof methods are topological and use a modified form of the configuration space/test map scheme. We obtain optimal results when r is a power of two.