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Technical Perspective: Isolating a Matching When Your Coins Go Missing


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Matchings in bipartite graphs play a foundational role in a variety of mathematical, scientific, and engineering disciplines—from Frobenius' work on the determinants of matrices, Gale and Shapley's influential paper on stable marriages and college admissions, Tolstoi and Kantorovich's work on the optimal transportation problem, to the online world where advertisements are being matched to users billions of times a day. As a consequence, algorithms for finding matchings in bipartite graphs also have a century-old history and the pursuit of efficient algorithms for this problem has led to major achievements in computer science and optimization.

In the 1980s, with the growing availability of parallelizable computer architectures, the study of whether one can parallelize algorithms for fundamental problems gained significant momentum. An efficient parallel algorithm would distribute the work on several processors in a manner that keeps the longest sequence of dependent tasks among processors small—ideally, logarithmic in the size of the problem. Several basic problems such as multiplying matrices, solving a system of equations and computing shortest paths in graphs already had such parallel algorithms.


 

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