Column-generation based bounds for the Homogeneous Areas Problem

Given an undirected graph and a collection of vertex subsets with suitable costs, we consider the problem of partitioning the graph into subgraphs of limited cost, splitting as little as possible the given subsets among different subgraphs. This problem originates from the organization of a region (the graph) including several towns (the vertices) into administrative areas (the subgraphs). The officers assigned to each area take care of activities which involve several towns at a time (the subsets). An activity involving towns from more areas engages the officers of all those areas, leading to redundancies which must be minimized.