Solving Linear Programs in MapReduce

Most interesting discrete optimization problems are NP-hard, thus no efficient algorithm to find optimal solution to such problems is likely to exist. Linear programming plays a central role in design and analysis of many approximation algorithms. However, linear program instances in real-world applications grow enormously. In this thesis, we study the Awerbuch-Khandekar parallel algorithm for approximating linear programs, provide strategies for efficient realization of the algorithm in MapReduce, and discuss methods to improve its performance in practice. Further, we characterize numerical properties of the algorithm by comparing it with partially-distributed optimization methods. Finally, we evaluate the algorithm on a weighted maximum satisfiability problem generated by SOFIE knowledge extraction framework on the complete Academic Corpus.

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