2 research outputs found
A Faster Algorithm for Fully Dynamic Betweenness Centrality
We present a new fully dynamic algorithm for maintaining betweenness
centrality (BC) of vertices in a directed graph with positive edge
weights. BC is a widely used parameter in the analysis of large complex
networks. We achieve an amortized time per update,
where and bounds the number of distinct edges that lie on
shortest paths through any single vertex. This result improves on the amortized
bound for fully dynamic BC in [Pontecorvi-Ramachandran2015] by a logarithmic
factor. Our algorithm uses new data structures and techniques that are
extensions of the method in the fully dynamic algorithm in Thorup [Thorup2004]
for APSP in graphs with unique shortest paths. For graphs with ,
our algorithm matches the fully dynamic APSP bound in [Thorup2004], which holds
for graphs with , since it assumes unique shortest paths.Comment: The current revision (v3) includes minor changes in the Introduction.
There is no change to the main result. A brief summary of this paper will
appear in Proc. ISAAC 2015, in a paper by the authors entitled "Fully Dynamic
Betweenness Centrality''. arXiv admin note: text overlap with arXiv:1412.385
Approximating Betweenness Centrality in Fully-dynamic Networks
Betweenness is a well-known centrality measure that ranks the nodes of a
network according to their participation in shortest paths. Since an exact
computation is prohibitive in large networks, several approximation algorithms
have been proposed. Besides that, recent years have seen the publication of
dynamic algorithms for efficient recomputation of betweenness in networks that
change over time. In this paper we propose the first betweenness centrality
approximation algorithms with a provable guarantee on the maximum approximation
error for dynamic networks. Several new intermediate algorithmic results
contribute to the respective approximation algorithms: (i) new upper bounds on
the vertex diameter, (ii) the first fully-dynamic algorithm for updating an
approximation of the vertex diameter in undirected graphs, and (iii) an
algorithm with lower time complexity for updating single-source shortest paths
in unweighted graphs after a batch of edge actions. Using approximation, our
algorithms are the first to make in-memory computation of betweenness in
dynamic networks with millions of edges feasible. Our experiments show that our
algorithms can achieve substantial speedups compared to recomputation, up to
several orders of magnitude. Moreover, the approximation accuracy is usually
significantly better than the theoretical guarantee in terms of absolute error.
More importantly, for reasonably small approximation error thresholds, the rank
of nodes is well preserved, in particular for nodes with high betweenness.Comment: arXiv admin note: substantial text overlap with arXiv:1504.07091,
arXiv:1409.624