A Tutorial on Clique Problems in Communications and Signal Processing

Since its first use by Euler on the problem of the seven bridges of K\"onigsberg, 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, the paper 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 non-orthogonal 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

Parallel (k)(k)-Clique Community Detection on Large-Scale Networks

The analysis of real-world complex networks has been the focus of recent research. Detecting communities helps in uncovering their structural and functional organization. Valuable insight can be obtained by analyzing the dense, overlapping, and highly interwoven k-clique communities. However, their detection is challenging due to extensive memory requirements and execution time. In this paper, we present a novel, parallel k-clique community detection method, based on an innovative technique which enables connected components of a network to be obtained from those of its subnetworks. The novel method has an unbounded, user-configurable, and input-independent maximum degree of parallelism, and hence is able to make full use of computational resources. Theoretical tight upper bounds on its worst case time and space complexities are given as well. Experiments on real-world networks such as the Internet and the World Wide Web confirmed the almost optimal use of parallelism (i.e., a linear speedup). Comparisons with other state-of-the-art k-clique community detection methods show dramatic reductions in execution time and memory footprint. An open-source implementation of the method is also made publicly available

Community Detection In Social Networks Using Parallel Clique-finding Ants

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Bilişim Enstitüsü, 2010Thesis (M.Sc.) -- İstanbul Technical University, Institute of Informatics, 2010İnternet ağının sürekli artan popülaritesiyle birlikte, insanlar daha çok bilgiyi ağ üzerinden dünyanın geri kalanıyla paylaşmaya ve geliştirmeye başladılar; buna bağlı olarak farklı disiplinlerde sosyal ağların analizi konusu da popüler hale geldi. Günümüzde sosyal ağlar üzerinde bulunan topluluk yapılarının tespiti, bilgisayar bilimleri açısından da önem kazandı. Bu amaçla kullanılan topluluk bulma algoritmaları iyi sonuçlar üretse de, büyük ölçekli sosyal ağlarda işlem karmaşıklığı ve buna bağlı ölçeklendirme konusunda yetersiz kalmaktadır. Bu tezin ana amacı, elde bulunan sosyal ağ çizgesini, çizgenin ana özelliklerini koruyarak daha küçük bir hale indirgemek, dolayısıyla topluluk bulma algoritmalarının verimini çözüm kalitesinden kayıp olmadan arttırmaktır. Bu çalışmada Karınca Kolonisi İyileştirme yöntemi sayesinde yarı bağlı alt çizgeler bulunmakta ve bu alt çizgeler ile ana çizge daha küçük bir hale indirgenmekte, son olarak indirgenmiş çizge üzerinde topluluk bulma algoritmaları koşturulmaktadır. Çeşitli sosyal ağ çizgeleri üzerinde koşulan testlerin sonuçları, uygulanan indirgeme yöntemi sonrasında topluluk bulma algoritmalarının çalışma sürelerinde iyileşme gözlenmiş, buna bağlı olarak indirgenme sonrasında çözüm kalitesinin de korunduğu tespit edilmiştir.Attractiveness of social network analysis as a research topic in many different disciplines is growing in parallel to the continuous growth of the Internet, which allows people to share and collaborate more. Nowadays, detection of community structures, which may be established on social networks, is a popular topic in Computer Science. High computational costs and non-scalability on large-scale social networks are the biggest drawbacks of popular community detection methods. The main aim of this thesis is to reduce the original network graph to a maintainable size so that computational costs decrease without loss of solution quality, thus increasing scalability on such networks. In this study, we focus on Ant Colony Optimization techniques to find quasi-cliques in the network and assign these quasi-cliques as nodes in a reduced graph to use with community detection algorithms. Experiments are performed on commonly used social networks with the addition of several large-scale networks. Based on the experimental results on various sized social networks, we may say that the execution times of the community detection methods are decreased while the overall quality of the solution is preserved.Yüksek LisansM.Sc