The VC-dimension of set systems defined by graphs
Discrete Applied Mathematics
Fast Estimation of Diameter and Shortest Paths (Without Matrix Multiplication)
SIAM Journal on Computing
Improved bounds on the sample complexity of learning
Journal of Computer and System Sciences
Bi-directional and heuristic search in path problems
Bi-directional and heuristic search in path problems
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Bidirectional heuristic search reconsidered
Journal of Artificial Intelligence Research
Routing betweenness centrality
Journal of the ACM (JACM)
Approximating betweenness centrality
WAW'07 Proceedings of the 5th international conference on Algorithms and models for the web-graph
Networks: An Introduction
Relative (p,ε)-Approximations in Geometry
Discrete & Computational Geometry
VC-dimension and shortest path algorithms
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Fast and simple approximation of the diameter and radius of a graph
WEA'06 Proceedings of the 5th international conference on Experimental Algorithms
Online sampling of high centrality individuals in social networks
PAKDD'10 Proceedings of the 14th Pacific-Asia conference on Advances in Knowledge Discovery and Data Mining - Volume Part I
k-Centralities: local approximations of global measures based on shortest paths
Proceedings of the 21st international conference companion on World Wide Web
Foundations of Machine Learning
Foundations of Machine Learning
Hi-index | 0.00 |
Betweenness centrality is a fundamental measure in social network analysis, expressing the importance or influence of individual vertices in a network in terms of the fraction of shortest paths that pass through them. Exact computation in large networks is prohibitively expensive and fast approximation algorithms are required in these cases. We present two efficient randomized algorithms for betweenness estimation. The algorithms are based on random sampling of shortest paths and offer probabilistic guarantees on the quality of the approximation. The first algorithm estimates the betweenness of all vertices: all approximated values are within an additive factor ɛ from the real values, with probability at least 1-δ. The second algorithm focuses on the top-K vertices with highest betweenness and approximate their betweenness within a multiplicative factor ɛ, with probability at least $1-δ. This is the first algorithm that can compute such approximation for the top-K vertices. We use results from the VC-dimension theory to develop bounds to the sample size needed to achieve the desired approximations. By proving upper and lower bounds to the VC-dimension of a range set associated with the problem at hand, we obtain a sample size that is independent from the number of vertices in the network and only depends on a characteristic quantity that we call the vertex-diameter, that is the maximum number of vertices in a shortest path. In some cases, the sample size is completely independent from any property of the graph. The extensive experimental evaluation that we performed using real and artificial networks shows that our algorithms are significantly faster and much more scalable as the number of vertices in the network grows than previously presented algorithms with similar approximation guarantees.