Fair distribution of bundles

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