Abstract
We present an incremental algorithm that updates the betweenness centrality (BC) score of all vertices in a graph G when a new edge is added to G, or the weight of an existing edge is reduced. Our incremental algorithm runs in O(v * · n) time, where v * is bounded by m *, the number of edges that lie on a shortest path in G. We achieve the same bound for the more general incremental vertex update problem. Even for a single edge update, our incremental algorithm is the first algorithm that is provably faster on sparse graphs than recomputing with the well-known static Brandes algorithm. It is also likely to be much faster than Brandes on dense graphs since m * is often close to linear in n. Our incremental algorithm is very simple, and we give an efficient cache-oblivious implementation that incurs O(n · sort(v *)) cache misses, where sort is a well-known measure for caching efficiency.
This work was supported in part by NSF grants CCF-0830737 and CCF-1320675.
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Nasre, M., Pontecorvi, M., Ramachandran, V. (2014). Betweenness Centrality – Incremental and Faster. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds) Mathematical Foundations of Computer Science 2014. MFCS 2014. Lecture Notes in Computer Science, vol 8635. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44465-8_49
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