I/O efficient computation of First Order Markov Measures for Large and Evolving Graphs

Date of Submission: 
July 21, 2008
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First order Markov measures, such as PageRank, have gained significance as relevance measure in domains where data is represented as a graph. The large scale of such graphs in real world, such as the World Wide Web has given rise to computing challenges of such measures. In this paper, we address the challenges of computing such First-order Markov measure, considering PageRank as the example of such a measure. We address two challenging computational scenarios for PageRank: (a) computation for a large single graph at a given time instance and (b) incremental computation for large evolving graphs. We achieve efficiency by reducing the problem size and reducing the number of iterations to compute. For (a) we bin the nodes in different partitions and for the subgraph formed by each of these partitions we use the nature of the firstorder Markov model to break down the problem of computation. For (b) we propose a method to accommodate the changed edges and nodes into new partitions and existing partitions and identify the subset of partitions for which recomputation is necessary. For each identified partition we use an incremental approach to compute the measure in expedited manner. Our results show significant reduction in time for computing for our approaches to both these problems.