Efficient and Exact Local Search for Random Walk Based Top-K Proximity Query in Large Graphs

Efficient and Exact Local Search for Random Walk Based Top-K Proximity Query in Large Graphs

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Top- k proximity query in large graphs is a fundamental problem with a wide range of applications. Various random walk based measures have been proposed to measure the proximity between different nodes. Although these measures are effective, efficiently computing them on large graphs is a challenging task. An efficient and exact local search method is developed, FLoS (Fast Local Search), for top- k proximity query in large graphs. FLoS guarantees the exactness of the solution. Moreover, it can be applied to a variety of commonly used proximity measures. FLoS is based on the no local optimum property of proximity measures. We show that many measures have no local optimum. Utilizing this property, we introduce several operations to manipulate transition probabilities and develop tight lower and upper bounds on the proximity values. The lower and upper bounds monotonically converge to the exact proximity value when more nodes are visited.

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