Pruning based Distance Sketches with Provable Guarantees on Random Graphs

TL;DR

This paper introduces an efficient preprocessing algorithm for creating landmark-based distance sketches on large graphs, providing strong theoretical guarantees and improved practical performance over existing methods.

Contribution

It presents a novel landmark-based distance sketching algorithm with provable guarantees and demonstrates its effectiveness on various real-world and random graph models.

Findings

Reduces number of landmarks needed for accurate distance estimation

Achieves faster preprocessing times compared to previous approaches

Provides tight theoretical bounds for Erdős-Rényi and power law graphs

Abstract

Measuring the distances between vertices on graphs is one of the most fundamental components in network analysis. Since finding shortest paths requires traversing the graph, it is challenging to obtain distance information on large graphs very quickly. In this work, we present a preprocessing algorithm that is able to create landmark based distance sketches efficiently, with strong theoretical guarantees. When evaluated on a diverse set of social and information networks, our algorithm significantly improves over existing approaches by reducing the number of landmarks stored, preprocessing time, or stretch of the estimated distances. On Erd\"{o}s-R\'{e}nyi graphs and random power law graphs with degree distribution exponent $2 < \beta < 3$, our algorithm outputs an exact distance data structure with space between $\Theta(n^{5/4})$ and $\Theta(n^{3/2})$ depending on the value of $\beta$, where $n$ is the number of vertices. We complement the algorithm with tight lower bounds for Erdos-Renyi graphs and the case when $\beta$ is close to two.