## Balanced Allocation with Succinct Representation

author: Saeed Alaei, Department of Computer Science, University of Maryland
published: Oct. 1, 2010,   recorded: July 2010,   views: 283
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# Description

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.