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Preface
Contents
Acronyms
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
1.2 Hypergraph Coloring
1.2.1 Basic Kinds of Hypergraph Coloring
1.2.2 Greedy Algorithm for Hypergraph Coloring
1.3 Hypergraph Clustering
1.3.1 Hypergraph Clustering Problem
1.3.2 Clustering Algorithm
References
2 Radio Resource Allocation for Device-to-Device Underlay Communications
2.1 Introduction
2.2 System Model and Problem Formulation
2.2.1 System Model
2.2.2 Problem Formulation
2.3 Traditional Graph Based Channel Allocation
2.3.1 Graph Construction
2.3.2 Channel Allocation Algorithm
2.4 Hypergraph Based Channel Allocation
2.4.1 Hypergraph Construction
2.4.1.1 Independent Interferer Recognition
2.4.1.2 Cumulative Interferer Recognition
2.4.2 Hypergraph Coloring Algorithm
2.5 Property Analysis
2.6 Simulation Results
2.7 Summary
References
3 Resource Allocation for Cross-Cell Device-to-Device Communications
3.1 Introduction
3.2 System Model and Problem Formulation
3.2.1 System Model
3.2.2 Cross-Cell D2D Communications
3.2.3 Problem Formulation
3.3 Hypergraph Based Algorithm
3.3.1 Hypergraph Construction
3.3.1.1 Pairwise Edges Formation
3.3.1.2 Hyperedge Formation
3.3.2 Hypergraph Clustering
3.3.3 Convergence
3.3.4 Alternating Optimization
3.4 Simulation Results
3.5 Summary
References
4 Conclusions and Future Works
4.1 Conclusions
4.2 Other Applications
4.2.1 Socially-Aware Content Delivery Networks
4.2.2 Codebook Assignment Using SCMA
4.2.3 Heterogeneous Cloud Radio Access Networks
4.2.4 Smartphone Sensing
References
SPRINGER BRIEFS IN ELECTRICAL AND COMPUTER ENGINEERING HongliangZhang LingyangSong ZhuHan YingjunZhang 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 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
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 vii
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