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. We present an O(n)-time algorithm for performing apportionment under a large class of highest averages methods. Our algorithm works for all highest averages methods used in practice.
@article{arxiv.1409.2603,
title = {Linear-time Algorithms for Proportional Apportionment},
author = {Zhanpeng Cheng and David Eppstein},
journal= {arXiv preprint arXiv:1409.2603},
year = {2014}
}