Partitioning and the online-world design problem for multi-player games

A problem encountered in online multi-player gaming communities involves the following: given a set of p players each of whom has strength p_j, and a set of m monsters, each of whom has strength m_i, is it possible to partition the players into groups such that each monster is assigned a group of players that is capable of overcoming said monster? A feasibility algorithm for the class restricted version of the problem, which has computational complexity O(p^2(q-1) log₂m) is developed, where q is the number of classes.