Diameter And Rumour Spreading In Real World Network Models
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Diameter And Rumour Spreading In Real World Network Models
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Author : Abbas Mehrabian
language : en
Publisher:
Release Date : 2015
Diameter And Rumour Spreading In Real World Network Models written by Abbas Mehrabian and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
The so-called 'small-world phenomenon', observed in many real-world networks, is that there is a short path between any two nodes of a network, whose length is much smaller that the network's size, typically growing as a logarithmic function. Several mathematical models have been defined for social networks, the WWW, etc., and this phenomenon translates to proving that such models have a small diameter. In the first part of this thesis, we rigorously analyze the diameters of several random graph classes that are introduced specifically to model complex networks, verifying whether this phenomenon occurs in them. In Chapter 3 we develop a versatile technique for proving upper bounds for diameters of evolving random graph models, which is based on defining a coupling between these models and variants of random recursive trees. Using this technique we prove, for the first time, logarithmic upper bounds for the diameters of seven well known models. This technique gives unified simple proofs for known results, provides lots of new ones, and will help in proving many of the forthcoming network models are small-world. Perhaps, for any given model, one can come up with an ad hoc argument that the diameter is O(log n), but it is interesting that a unified technique works for such a wide variety of models, and our first major contribution is introducing such a technique. In Chapter 4 we estimate the diameter of random Apollonian networks, a class of random planar graphs. We also give lower and upper bounds for the length of their longest paths. In Chapter 5 we study the diameter of another random graph model, called the random surfer Web-graph model. We find logarithmic upper bounds for the diameter, which are almost tight in the special case when the growing graph is a tree. Although the two models are quite different, surprisingly the same engine is used for proving these results, namely the powerful technique of Broutin and Devroye (Large deviations for the weighted height of an extended class of trees, Algorithmica 2006) for analyzing weighted heights of random trees, which we have adapted and applied to the two random graph models. Our second major contribution is demonstrating the flexibility of this technique via providing two significant applications. In the second part of the thesis, we study rumour spreading in networks. Suppose that initially a node has a piece of information and wants to spread it to all nodes in a network quickly. The problem of designing an efficient protocol performing this task is a fundamental one in distributed computing and has applications in maintenance of replicated databases, broadcasting algorithms, analyzing news propagation is social networks and the spread of viruses on the Internet. Given a rumour spreading protocol, its spread time is the time it takes for the rumour to spread in the whole graph. In Chapter 6 we prove several tight lower and upper bounds for the spread times of two well known randomized rumour spreading protocols, namely the synchronous push&pull protocol and the asynchronous push&pull protocol. In particular, we show the average spread time in both protocols is always at most linear. In Chapter 7 we study the performance of the synchronous push&pull protocol on random k-trees. We show that a.a.s. after a polylogarithmic amount of time, 99 percent of the nodes are informed, but to inform all vertices, a polynomial amount of time is required. Our third majoc contribution is giving analytical proofs for two experimentally verified statements: firstly, the asynchronous push&pull protocol is typically faster than its synchronous variant, and secondly, it takes considerably more time to inform the last 1 percent of the vertices in a social network than the first 99 percent. We hope that our work on the asynchronous push&pull protocol attracts attention to this fascinating model.
Complex Networks Xv
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Author : Federico Botta
language : en
Publisher: Springer Nature
Release Date :
Complex Networks Xv written by Federico Botta and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Automata Languages And Programming
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Author : Magnús M. Halldórsson
language : en
Publisher: Springer
Release Date : 2015-06-19
Automata Languages And Programming written by Magnús M. Halldórsson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-19 with Computers categories.
The two-volume set LNCS 9134 and LNCS 9135 constitutes the refereed proceedings of the 42nd International Colloquium on Automata, Languages and Programming, ICALP 2015, held in Kyoto, Japan, in July 2015. The 143 revised full papers presented were carefully reviewed and selected from 507 submissions. The papers are organized in the following three tracks: algorithms, complexity, and games; logic, semantics, automata and theory of programming; and foundations of networked computation: models, algorithms and information management.
Statistical Analysis Of Network Data
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Author : Eric D. Kolaczyk
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-20
Statistical Analysis Of Network Data written by Eric D. Kolaczyk and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-20 with Computers categories.
In recent years there has been an explosion of network data – that is, measu- ments that are either of or from a system conceptualized as a network – from se- ingly all corners of science. The combination of an increasingly pervasive interest in scienti c analysis at a systems level and the ever-growing capabilities for hi- throughput data collection in various elds has fueled this trend. Researchers from biology and bioinformatics to physics, from computer science to the information sciences, and from economics to sociology are more and more engaged in the c- lection and statistical analysis of data from a network-centric perspective. Accordingly, the contributions to statistical methods and modeling in this area have come from a similarly broad spectrum of areas, often independently of each other. Many books already have been written addressing network data and network problems in speci c individual disciplines. However, there is at present no single book that provides a modern treatment of a core body of knowledge for statistical analysis of network data that cuts across the various disciplines and is organized rather according to a statistical taxonomy of tasks and techniques. This book seeks to ll that gap and, as such, it aims to contribute to a growing trend in recent years to facilitate the exchange of knowledge across the pre-existing boundaries between those disciplines that play a role in what is coming to be called ‘network science.
Stochastic Processes And Applications
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Author : Sergei Silvestrov
language : en
Publisher: Springer
Release Date : 2018-12-05
Stochastic Processes And Applications written by Sergei Silvestrov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-05 with Mathematics categories.
This book highlights the latest advances in stochastic processes, probability theory, mathematical statistics, engineering mathematics and algebraic structures, focusing on mathematical models, structures, concepts, problems and computational methods and algorithms important in modern technology, engineering and natural sciences applications. It comprises selected, high-quality, refereed contributions from various large research communities in modern stochastic processes, algebraic structures and their interplay and applications. The chapters cover both theory and applications, illustrated by numerous figures, schemes, algorithms, tables and research results to help readers understand the material and develop new mathematical methods, concepts and computing applications in the future. Presenting new methods and results, reviews of cutting-edge research, and open problems and directions for future research, the book serves as a source of inspiration for a broad spectrum of researchers and research students in probability theory and mathematical statistics, applied algebraic structures, applied mathematics and other areas of mathematics and applications of mathematics. The book is based on selected contributions presented at the International Conference on “Stochastic Processes and Algebraic Structures – From Theory Towards Applications” (SPAS2017) to mark Professor Dmitrii Silvestrov’s 70th birthday and his 50 years of fruitful service to mathematics, education and international cooperation, which was held at Mälardalen University in Västerås and Stockholm University, Sweden, in October 2017.
Random Graphs And Complex Networks
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Author : Remco van der Hofstad
language : en
Publisher: Cambridge University Press
Release Date : 2017
Random Graphs And Complex Networks written by Remco van der Hofstad and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Computers categories.
This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.
Epidemics And Rumours In Complex Networks
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Author : Moez Draief
language : en
Publisher: Cambridge University Press
Release Date : 2009-12-03
Epidemics And Rumours In Complex Networks written by Moez Draief and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-03 with Mathematics categories.
Information propagation through peer-to-peer systems, online social systems, wireless mobile ad hoc networks and other modern structures can be modelled as an epidemic on a network of contacts. Understanding how epidemic processes interact with network topology allows us to predict ultimate course, understand phase transitions and develop strategies to control and optimise dissemination. This book is a concise introduction for applied mathematicians and computer scientists to basic models, analytical tools and mathematical and algorithmic results. Mathematical tools introduced include coupling methods, Poisson approximation (the Stein-Chen method), concentration inequalities (Chernoff bounds and Azuma-Hoeffding inequality) and branching processes. The authors examine the small-world phenomenon, preferential attachment, as well as classical epidemics. Each chapter ends with pointers to the wider literature. An ideal accompaniment for graduate courses, this book is also for researchers (statistical physicists, biologists, social scientists) who need an efficient guide to modern approaches to epidemic modelling on networks.
Gossip Algorithms
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Author : Devavrat Shah
language : en
Publisher: Now Publishers Inc
Release Date : 2009
Gossip Algorithms written by Devavrat Shah and has been published by Now Publishers Inc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Computers categories.
A systematic survey of many of these recent results on Gossip network algorithms.
Diffusion In Social Networks
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Author : Paulo Shakarian
language : en
Publisher: Springer
Release Date : 2015-09-16
Diffusion In Social Networks written by Paulo Shakarian and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-16 with Computers categories.
This book presents the leading models of social network diffusion that are used to demonstrate the spread of disease, ideas, and behavior. It introduces diffusion models from the fields of computer science (independent cascade and linear threshold), sociology (tipping models), physics (voter models), biology (evolutionary models), and epidemiology (SIR/SIS and related models). A variety of properties and problems related to these models are discussed including identifying seeds sets to initiate diffusion, game theoretic problems, predicting diffusion events, and more. The book explores numerous connections between social network diffusion research and artificial intelligence through topics such as agent-based modeling, logic programming, game theory, learning, and data mining. The book also surveys key empirical results in social network diffusion, and reviews the classic and cutting-edge research with a focus on open problems.
Networks
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Author : Mark Newman
language : en
Publisher: Oxford University Press
Release Date : 2010-03-25
Networks written by Mark Newman and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-25 with Computers categories.
This book brings together advances in mathematics, physics, computer science, biology and social network analysis to present a comprehensive picture of the scientific study of networks. The book includes discussion of computer networks, social networks, biological networks, and others, and an introduction to the mathematics of network theory.