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Hypergraph theory in wireless communication networks
Zhang H., Song L., Han Z., Zhang Y., Springer International Publishing, New York, NY, 2018. 62 pp. Type: Book (978-3-319604-67-1)
Date Reviewed: Jan 4 2019

This short publication really fits in the “SpringerBriefs” series. Despite the fact that the book could be considered a long paper, it may interest researchers in the applications of mathematics field. The book starts with an overview of hypergraph theory [1,2], including the basic definitions and theorems required to understand the proposed approach.

The introductory part concludes with mathematical methods, namely graph coloring and clustering algorithms in hypergraphs. These methods (the presented theoretical basis) will find application in the second part of the book.

The core issue of the book is how a cellular (mobile) network can be modeled using a weighted hypergraph. A weighted hypergraph is an extension of a hypergraph by associating a weight to each hyperedge and node. For the purpose at hand, the authors present a calculation method for modeling telecommunication tasks.

Next, the book presents the mapping of architecture elements of the cellular networks onto the weighted hypergraph structure and the proposed approach for the optimization problem within the network, namely the resource allocation problem. The brief book concludes with an analysis of the proposed hypergraph-based model and possible future developments.

The book is interesting, even for readers not involved in wireless networks research. It shows a systematic approach to the application of mathematical concepts and theories in telecommunications and information technology. The ideas raised are thought-provoking, and the approach may be customized for other fields, that is, mapping concepts onto hypergraphs, defining weights or other evaluation functions, and so on, thereby offering fruitful research directions.

Reviewer:  Bálint Molnár Review #: CR146371 (1904-0086)
1) Voloshin, V. I. Introduction to graph and hypergraph theory. Nova Science Publishers, Hauppauge, NY, 2009.
2) Bretto, A. Hypergraph theory: an introduction. Springer, Cham, Switzerland, 2013.
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