均衡的分配,简洁的表示

S. Alaei, Ravi Kumar, Azarakhsh Malekian, Erik Vee
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引用次数: 4

摘要

受保证交付在计算广告中的应用的启发,我们考虑了在供需双方设置下平衡分配的一般问题。我们的公式抓住了偏离被凸惩罚函数平衡的概念。虽然这个公式承认凸规划解决方案,但我们努力寻求更健壮和可扩展的算法。对于L1惩罚函数,我们得到了一种基于最小代价流的简单组合算法,并展示了如何预先计算线性信息量,使得沿任意边的分配可以在常数时间内近似。然后,我们通过求解一个凸代价流将我们的组合解扩展到任何凸函数。这些可扩展的方法可以应用于其他规定均衡分配的上下文中。我们研究了我们的算法在大型现实世界图上的性能,并在实践中证明了它们是高效、可扩展和鲁棒的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Balanced allocation with succinct representation
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 L1 penalty functions we obtain a simple combinatorial algorithm based on min-cost flow in graphs 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. 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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