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A Tutorial on Clique Problems in Communications and Signal Processing

Douik, Ahmed and Dahrouj, Hayssam and Al-Naffouri, Tareq Y. and Alouini, Mohamed-Slim (2020) A Tutorial on Clique Problems in Communications and Signal Processing. Proceedings of the IEEE, 108 (4). pp. 583-608. ISSN 0018-9219. https://resolver.caltech.edu/CaltechAUTHORS:20200327-123332936

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Abstract

Since its first use by Euler on the problem of the seven bridges of Königsberg, graph theory has shown excellent abilities in solving and unveiling the properties of multiple discrete optimization problems. The study of the structure of some integer programs reveals equivalence with graph theory problems making a large body of the literature readily available for solving and characterizing the complexity of these problems. This tutorial presents a framework for utilizing a particular graph theory problem, known as the clique problem, for solving communications and signal processing problems. In particular, this article aims to illustrate the structural properties of integer programs that can be formulated as clique problems through multiple examples in communications and signal processing. To that end, the first part of the tutorial provides various optimal and heuristic solutions for the maximum clique, maximum weight clique, and k-clique problems. The tutorial, further, illustrates the use of the clique formulation through numerous contemporary examples in communications and signal processing, mainly in maximum access for nonorthogonal multiple access networks, throughput maximization using index and instantly decodable network coding, collision-free radio-frequency identification networks, and resource allocation in cloud-radio access networks. Finally, the tutorial sheds light on the recent advances of such applications, and provides technical insights on ways of dealing with mixed discrete-continuous optimization problems.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/jproc.2020.2977595DOIArticle
ORCID:
AuthorORCID
Douik, Ahmed0000-0001-7791-9443
Dahrouj, Hayssam0000-0002-0737-6372
Al-Naffouri, Tareq Y.0000-0001-6955-4720
Alouini, Mohamed-Slim0000-0003-4827-1793
Additional Information:© 2020 IEEE. Manuscript received January 8, 2020; accepted February 22, 2020. Date of publication March 23, 2020; date of current version April 8, 2020. The authors would like to thank Ahmed K. Sultan Salem for his helpful discussions and valuable comments. They further extend their gratitude to the anonymous reviewers whose comments and suggestions helped improve the quality of this article. Hayssam Dahrouj would like to thank Effat University in Jeddah, Saudi Arabia, for funding the research reported in this article through the Research and Consultancy Institute.
Funders:
Funding AgencyGrant Number
Effat UniversityUNSPECIFIED
Subject Keywords:Communications; discrete optimization; graph theory clique problem; signal processing
Issue or Number:4
Record Number:CaltechAUTHORS:20200327-123332936
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200327-123332936
Official Citation:A. Douik, H. Dahrouj, T. Y. Al-Naffouri and M. Alouini, "A Tutorial on Clique Problems in Communications and Signal Processing," in Proceedings of the IEEE, vol. 108, no. 4, pp. 583-608, April 2020
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:102145
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:27 Mar 2020 19:43
Last Modified:16 Apr 2020 17:03

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