Abstract (EN)

We define a NP-hard clustered variant of the Set Covering Problem where subsets are partitioned into K clusters and a fixed cost is paid for selecting at least one subset in a given cluster. This variant can reformulate as a master problem various multicommodity flow problems in transportation planning. We show that the problem is approximable within ratio (1 + ǫ)(e/e− 1)H(q), where q is the maximum number of elements covered by a cluster and H(q) = Pq i=1 1 i .