Abstract
In this paper, we consider the problem of partitioning a given collection of node sets into k collections such that the average size of collections is the largest, where the size of a collection is defined as the cardinarity of the union of the subsets contained in the collection. More concretely, we give an upper bound on the performance ratio of an approximation algorithm proposed by Abrams et al., which is known to have a performance ratio of at least 1-1/e≅0.6321 where e is Napier's constant. The proposed upper bound is 1-(2-d+1√2)d+1/2 for any d≥1 provided that k=o(n) which approaches to 0.75 as d increases.
