Towards Classifying the Polynomial-Time Solvability of Temporal Betweenness Centrality

@article{Rymar2021TowardsCT,
  title={Towards Classifying the Polynomial-Time Solvability of Temporal Betweenness Centrality},
  author={Maciej Rymar and Hendrik Molter and Andr{\'e} Nichterlein and Rolf Niedermeier},
  journal={ArXiv},
  year={2021},
  volume={abs/2105.13055}
}
In static graphs, the betweenness centrality of a graph vertex measures how many times this vertex is part of a shortest path between any two graph vertices. Betweenness centrality is efficiently computable and it is a fundamental tool in network science. Continuing and extending previous work, we study the efficient computability of betweenness centrality in temporal graphs (graphs with fixed vertex set but time-varying arc sets). Unlike in the static case, there are numerous natural notions… 
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Background Citations
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3 Citations

Temporal Connectivity: Coping with Foreseen and Unforeseen Delays
TLDR
This work gives polynomial-time algorithms for the two extreme cases: delays known before departure and delays occurring without prior warning (the latter leading to a two-player game scenario).
ONBRA: Rigorous Estimation of the Temporal Betweenness Centrality in Temporal Networks
TLDR
This work presents, the first sampling-based approximation algorithm for estimating the temporal betweenness centrality values of the nodes in a temporal network, providing rigorous probabilistic guarantees on the quality of its output.
Counting Temporal Paths
TLDR
This work initiates a systematic study of the prameterised and approximation complexity of #Temporal Path, the problem of counting all temporal paths between a fixed pair of vertices; like the problems of counting foremost and fastest temporal paths, it is #P-hard in general.

References

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