Average Distance Queries through Weighted Samples in Graphs and Metric Spaces: High Scalability with Tight Statistical Guarantee

The average distance from a node to all other nodes in a graph, or from a query point in a metric space to a set of points, is a fundamental quantity in data analysis. The inverse of the average distance, known as the (classic) closeness centrality of a node, is a popular importance measure in the study of social networks. We develop novel structural insights on the sparsifiability of the distance relation via weighted sampling. Based on that, we present highly practical algorithms with strong statistical guarantees for fundamental problems. We show that the average distance (and hence the centrality) for all nodes in a graph can be estimated using O( −2 ) single-source distance computations. For a set V of n points in a metric space, we show that after preprocessing which uses O(n) distance computations we can compute a weighted sample S ⊂ V of size O( −2 ) such that the average distance from any query point v to V can be estimated from the distances from v to S. Finally, we s...

• Type: Journal
• Year: 2015
• Where: APPROX
• Authors: Shiri Chechik, Edith Cohen, Haim Kaplan
• Keywords: Algorithms, APPROX 2015