SPRINGER BRIEFS IN
ELECTRICAL AND COMPUTER ENGINEERING
Hongliang Zhang
Lingyang Song
Zhu Han
Yingjun Zhang
Hypergraph
Theory in
Wireless
Communication
Networks
123
SpringerBriefs in Electrical and Computer
Engineering
More information about this series at http://www.springer.com/series/10059
Hongliang Zhang • Lingyang Song Zhu Han
Yingjun Zhang
Hypergraph Theory in
Wireless Communication
Networks
123
Hongliang Zhang
Peking University
Beijing, China
Zhu Han
University of Houston
Houston, TX, USA
Lingyang Song
Peking University
Beijing, China
Yingjun Zhang
The Chinese University of Hong Kong
Hong Kong, Hong Kong
ISSN 2191-8112
SpringerBriefs in Electrical and Computer Engineering
ISBN 978-3-319-60467-1
DOI 10.1007/978-3-319-60469-5
ISSN 2191-8120 (electronic)
ISBN 978-3-319-60469-5 (eBook)
Library of Congress Control Number: 2017945358
© The Author(s) 2018
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Preface
With the explosive traffic demand and dense mobile devices, a new generation
of cellular networks is required to support resource sharing among multiple
mobile devices and manage their collisions properly. In this book, we focus on
communication systems in which network devices are allowed to reuse the same
resource so as to improve the overall performance. For example, mobile users with
sparse code multiple access (SCMA) share the same codebook, or ultra-dense small
cells with massive multiple-input-multiple-output (MIMO) share the same limited
pilot sequences.
Conventionally, considering the topology of network devices, graph theory is
a useful tool to seek the solutions of the resource sharing problem. In the graph
representation of cellular network, each vertex represents a network device, and an
edge exists between two vertices if they collide when sharing the same resource.
Therefore, the resource allocation problem corresponds to finding the independent
set in which the devices do not collide. By modeling the pairwise relations, the
overall system performance increases.
However, in many scenarios of future wireless systems, the network needs
to coordinate multiple devices in order to further improve the utilization of the
scarce spectrum resources, and thus, the graph model is not accurate in modeling
the relation among multiple devices. For example, in the subchannel allocation
problem in non-orthogonal multiple access (NOMA), the mobile users share the
same subchannel with multiple mobile users, and thus, these mobile users will
bring cumulative interference, which cannot be captured by traditional graph. In this
book, we introduce a mathematical framework from hypergraph theory, in which a
hyperedge can be a subset of the vertex set. It provides a useful analytical tool for the
readers to analyze how the relations among multiple mobile users affect the system
performance, and thus, can be applied to address the resource sharing scenarios in
future wireless networks.
First, in Chap. 1, we introduce the basic preliminaries of hypergraph theory
in general and develop two hypergraph-based polynomial algorithms, i.e., hyper-
graph coloring and hypergraph clustering. Then, in Chaps. 2 and 3, we present
two emerging applications of hypergraph coloring and hypergraph clustering in
v
vi
Preface
Device-to-Device (D2D) underlay communication networks, respectively, in order
to show the advantages of hypergraph theory compared with the traditional graph
theory. Finally, in Chap. 4, we discuss the limitations of using hypergraph theory in
future wireless networks and briefly present some other potential applications.
Beijing, China
Beijing, China
Houston, TX, USA
Hong Kong, Hong Kong
Hongliang Zhang
Lingyang Song
Zhu Han
Yingjun Zhang
Contents
1 Basics of Hypergraph Theory ...............................................
1.1 Basic Hypergraph Concepts .............................................
1.1.1 Preliminary Definitions ..........................................
1.1.2
Incidence and Duality ...........................................
1.1.3 Basic Hypergraph Operations ...................................
1.1.4 Subhypergraphs ..................................................
1
1
1
3
5
8
1.2 Hypergraph Coloring .................................................... 11
1.2.1 Basic Kinds of Hypergraph Coloring ........................... 11
1.2.2 Greedy Algorithm for Hypergraph Coloring ................... 13
1.3 Hypergraph Clustering ................................................... 14
1.3.1 Hypergraph Clustering Problem ................................ 15
1.3.2 Clustering Algorithm ............................................ 16
References ...................................................................... 19
2 Radio Resource Allocation for Device-to-Device Underlay
Communications .............................................................. 21
2.1 Introduction .............................................................. 21
2.2 System Model and Problem Formulation ............................... 22
2.2.1 System Model .................................................... 22
2.2.2 Problem Formulation ............................................ 24
2.3 Traditional Graph Based Channel Allocation........................... 25
2.3.1 Graph Construction .............................................. 25
2.3.2 Channel Allocation Algorithm .................................. 26
2.4 Hypergraph Based Channel Allocation ................................. 26
2.4.1 Hypergraph Construction........................................ 27
2.4.2 Hypergraph Coloring Algorithm ................................ 29
2.5 Property Analysis ........................................................ 31
2.6 Simulation Results ....................................................... 33
2.7 Summary ................................................................. 37
References ...................................................................... 38
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