# 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} }

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

Fully Dynamic All Pairs All Shortest Paths

- Computer ScienceArXiv
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This work presents a fully dynamic algorithm for the all pairs all shortest paths (APASP) problem, which maintains all of the multiple shortest paths for every vertex pair in a directed graph G=(V,E) with a positive real weight on each edge.

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These algorithms match the fully dynamic all pairs shortest paths (APSP) bounds of Demetrescu and Italiano [8] and Thorup [28] for unique shortest paths, where \(\nu ^*=n-1\).

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