Towards Classifying the Polynomial-Time Solvability of Temporal Betweenness Centrality
Abstract
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 of being a "shortest" temporal path (walk). Depending on which notion is used, it was already observed that the problem is #P-hard in some cases while polynomial-time solvable in others. In this conceptual work, we contribute towards classifying what a "shortest path (walk) concept" has to fulfill in order to gain polynomial-time computability of temporal betweenness centrality.
Cite
@article{arxiv.2105.13055,
title = {Towards Classifying the Polynomial-Time Solvability of Temporal Betweenness Centrality},
author = {Maciej Rymar and Hendrik Molter and André Nichterlein and Rolf Niedermeier},
journal= {arXiv preprint arXiv:2105.13055},
year = {2021}
}