2017/12/23 by Hongyang Zhang, Zhang, Hongyang, Huacheng Yu +3
Computer Science · Physics and Astronomy · #Complex Network Analysis Techniques #Data Management and Algorithms #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Physics and Society (physics.soc-ph) #Probability (math.PR) #Social and Information Networks (cs.SI) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1712.08709
openalex publication_date 2017/12/23 · openalex created_date 2019/09/05 · openalex updated_date 2026/07/28
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 Erdös-Rényi graphs and random power law graphs with degree distribution exponent 2 < β< 3, our algorithm outputs an exact distance data structure with space between Θ(n5/4) and Θ(n3/2) depending on the value of β, where n is the number of vertices. We complement the algorithm with tight lower bounds for Erdos-Renyi graphs and the case when β is close to two.