The apportionment problem deals with the fair distribution of a discrete set of k indivisible resources (such as legislative seats) to n entities (such as parties or geographic subdivisions). Highest averages methods are a frequently used class of methods for solving this problem. Epstein presents an O(n)-time algorithm for performing apportionment under a large class of highest averages methods. The algorithm works for all highest averages methods used in practice. (Joint work with Zhanpeng Cheng.)