# Material Detail

## Balanced Allocation with Succinct Representation

This video was recorded at 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD), Washington 2010. Motivated by applications in guaranteed delivery in computational advertising, we consider the general problem of balanced allocation in a bipartite supply-demand setting. Our formulation captures the notion of deviation from being balanced by a convex penalty function. While this formulation admits a convex programming solution, we strive for more robust and scalable algorithms. For the case of $L_1$ penalty functions we obtain a simple combinatorial algorithm based on min-cost flow in graphs and show how to precompute a \emph{linear} amount of information such that the allocation along any edge can be approximated in \emph{constant} time. We then extend our combinatorial solution to any convex function by solving a convex cost flow. These scalable methods may have applications in other contexts stipulating balanced allocation. We study the performance of our algorithms on large real-world graphs and show that they are efficient, scalable, and robust in practice.

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