Abstract (EN)

A number of location problems in networks with nodal demand consist in finding a minimum-cost partition of nodes. In the minimum bounded-diameter spanning forest problem, the network is partitioned into a minimum number of trees such that the weighted diameter of every tree in the partition does not exceed a given bound B. This problem models applications such as dividing a sales area into a minimum number of regions so that a salesman should not drive more than B kilometers or hours for visiting any two customers in a region. We show that it is equivalent to finding a least set of points in the network such that the distance from the farthest demand node to the set is bounded, which is the converse version of the well-known absolute k-center problem. Finally, we adapt the greedy Set Covering heuristic to our problem using an approach called "master-slave", in order to prove approximability within log-factor.