Dynamic Shortest Path Algorithms for Hypergraphs

A hypergraph is a set V of vertices and a set of nonempty 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 probl...

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Bibliographic Details
Published in:IEEE/ACM transactions on networking Vol. 23; no. 6; pp. 1805 - 1817
Main Authors: Jianhang Gao, Qing Zhao, Wei Ren, Swami, Ananthram, Ramanathan, Ram, Bar-Noy, Amotz
Format: Journal Article
Language:English
Published: New York IEEE 01.12.2015
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Complement
Critical path
Dynamic
Dynamics
Electronic mail
Email
Graphs
Heuristic algorithms
hypergraph
hyperpath
IEEE transactions
Networks
Partitioning
Routing
shortest path
Shortest path problem
Shortest-path problems
Social network services
Time complexity
ISSN:1063-6692, 1558-2566
Online Access:Get full text
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Summary:A hypergraph is a set V of vertices and a set of nonempty 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. We analyze the time complexity of the proposed algorithms and perform simulation experiments for random geometric hypergraphs, energy efficient routing in multichannel multiradio networks, and the Enron email data set. The experiment with the Enron email data set illustrates the application of the proposed algorithms in social networks for identifying the most important actor and the latent social relationship based on the closeness centrality metric.
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ISSN:1063-6692
1558-2566
DOI:10.1109/TNET.2014.2343914