Fair Allocation with Succinct Representation

Motivated by applications in guaranteed delivery in computational advertising, we consider the general problem of fair allocation in a bipartite supply-demand setting. Our formulation captures the notion of deviation from fairness by a convex penalty function. While this formulation admits a convex programming solution, we strive for more timeand space-efficient algorithms. For the case of L1 penalty functions we obtain a simple combinatorial algorithm based on min-cost flow and show how to precompute a linear amount of information such that the allocation along any edge can be approximated in constant time. We then extend our combinatorial solution to any convex function by solving a convex cost flow. Our methods may have applications in other contexts stipulating fair allocation. We study the performance of our algorithms on a large real-world dataset and show that they are both efficient and effective in practice.