# Decremental All-Pairs ALL Shortest Paths and Betweenness Centrality

@article{Nasre2014DecrementalAA,
title={Decremental All-Pairs ALL Shortest Paths and Betweenness Centrality},
author={Meghana Nasre and Matteo Pontecorvi and Vijaya Ramachandran},
journal={ArXiv},
year={2014},
volume={abs/1411.4073}
}
• Published 14 November 2014
• Computer Science, Mathematics
• ArXiv
We consider the all pairs all shortest paths (APASP) problem, which maintains the shortest path dag rooted at every vertex in a directed graph $$G=(V,E)$$ with positive edge weights. For this problem we present a decremental algorithm (that supports the deletion of a vertex, or weight increases on edges incident to a vertex). Our algorithm runs in amortized $$O({\nu ^*}^2 \cdot \log n)$$ time per update, where $$n = |V|$$, and $${\nu ^*}$$ bounds the number of edges that lie on shortest paths…
11 Citations
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