Date of this Version
Taylor Spangler, 2013. Algorithms for Grid Graphs in the MapReduce Model. MS Thesis, University of Nebraska-Lincoln
The MapReduce programming paradigm has seen widespread use in analyzing large data sets. Often these large data sets can be formulated as graphs. Many algorithms, such as filtering based algorithms, are designed to work efficiently for dense graphs - graphs with substantially more number of edges than the number of vertices. These algorithms are not optimized for sparse graphs - graphs where the number of edges is of the same order as the number of vertices. However, sparse graphs are also common in big data sets. In this thesis we present algorithms for maximal matching, approximate edge covering, and approximate maximum weighted matching problems over grid graphs, a natural class of sparse graphs - graphs where the vertices and edges lie on a two dimensional integer grid. These algorithms take advantage of the inherent structure of grid graphs, thus making them more efficient than the known algorithms. In addition, in the case of maximum weighted matching, the algorithm presented gives a better approximation ratio than previous MapReduce algorithms.
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