TY - JOUR

T1 - A Tutorial on Clique Problems in Communications and Signal Processing

AU - Douik, Ahmed S.

AU - Dahrouj, Hayssam

AU - Al-Naffouri, Tareq Y.

AU - Alouini, Mohamed-Slim

N1 - KAUST Repository Item: Exported on 2020-10-01

PY - 2020/3/24

Y1 - 2020/3/24

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/662298

UR - https://ieeexplore.ieee.org/document/9044331/

UR - http://www.scopus.com/inward/record.url?scp=85082033027&partnerID=8YFLogxK

U2 - 10.1109/jproc.2020.2977595

DO - 10.1109/jproc.2020.2977595

M3 - Article

SP - 1

EP - 26

JO - Proceedings of the IEEE

JF - Proceedings of the IEEE

SN - 0018-9219

ER -