A hypergraph is a set V of vertices and a set of non-empty subsets of V, called hyperedges. Unlike graphs, hypergraphs can capture higher-order interactions in social and communication networks that go beyond a simple union of pairwise relationships. In this paper, we consider the shortest path problem in hypergraphs. We develop two algorithms for finding and maintaining the shortest hyperpaths in a dynamic network with both weight and topological changes. These two algorithms are the first to address the fully dynamic shortest path problem in a general hypergraph. They complement each other by partitioning the application space based on the nature of the change dynamics and the type of the hypergraph.
@article{arxiv.1202.0082,
title = {Dynamic Shortest Path Algorithms for Hypergraphs},
author = {Jianhang Gao and Qing Zhao and Wei Ren and Ananthram Swami and Ram Ramanathan and Amotz Bar-Noy},
journal= {arXiv preprint arXiv:1202.0082},
year = {2012}
}