The Routing of Complex Contagion in Kleinberg's Small-World Networks

نویسندگان

  • Wei Chen
  • Qiang Li
  • Xiaoming Sun
  • Jialin Zhang
چکیده

In Kleinberg’s small-world network model, strong ties are modeled as deterministic edges in the underlying base grid and weak ties are modeled as random edges connecting remote nodes. The probability of connecting a node u with node v through a weak tie is proportional to 1/|uv|, where |uv| is the grid distance between u and v and α ≥ 0 is the parameter of the model. Complex contagion refers to the propagation mechanism in a network where each node is activated only after k ≥ 2 neighbors of the node are activated. In this paper, we propose the concept of routing of complex contagion (or complex routing), where at each time step we can select one eligible node (nodes already having two active neighbors) to activate, with the goal of activating the pre-selected target node in the end. We consider decentralized routing scheme where only the links connected to already activated nodes are known to the selection strategy. We study the routing time of complex contagion and compare the result with simple routing and complex diffusion (the diffusion of complex contagion, where all eligible nodes are activated immediately in the same step with the goal of activating all nodes in the end). We show that for decentralized complex routing, the routing time is lower bounded by a polynomial in n (the number of nodes in the network) for all range of α both in expectation and with high probability (in particular, Ω(n 1 α+2 ) for α ≤ 2 and Ω(n α 2(α+2) ) for α > 2 in expectation). Our results indicate that complex routing is exponentially harder than both simple routing and complex diffusion at the sweetspot of α = 2.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Cascades and Myopic Routing in Nonhomogeneous Kleinberg's Small World Model

Kleinberg’s small world model [21] simulates social networks with both strong and weak ties. In his original paper, Kleinberg showed how the distribution of weak-ties, parameterized by γ, influences the efficacy of myopic routing on the network. Recent work on social influence by k-complex contagion models discovered that the distribution of weakties also impacts the spreading rate in a crucial...

متن کامل

Comparative Performance Analysis of AODV,DSR, TORA and OLSR Routing Protocols in MANET Using OPNET

Mobile Ad Hoc Networks (MANETs) are receiving a significant interest and are becoming very popular in the world of wireless networks and telecommunication. MANETs consist of mobile nodes which can communicate with each other without any infrastructure or centralized administration. In MANETs, the movement of nodes is unpredictable and complex; thus making the routing of the packets challenging....

متن کامل

Small-world Structure in Children’s Featured Semantic Networks

Background: Knowing the development pattern of children’s language is applicable in developmental psychology. Network models of language are helpful for the identification of these patterns.  Objectives: We examined the small-world properties of featured semantic networks of developing children. Materials & Methods: In this longitudinal study, the featured semantic networks of children aged 1...

متن کامل

Financial Crisis Contagion and the OPEC Oil Market

The impact of the financial crisis on the OPEC oil market is important to us as an important member of OPEC and an oil-exporting country with an oil-dependent economy. This study examines four networks, pre-financial crisis, US financial crisis, European debt crisis and post-financial crisis, using the contagion index and complex network for the period 2007-1-2 to 26-8-2019. The results show th...

متن کامل

A Survey of Solutions to Protect Against All Types of Attacks in Mobile Ad Hoc Networks

In recent years mobile networks have expanded dramatically, compared with other wireless networks. Routing protocols in these networks are designed with the assumption that there is no attacker node, so routing protocols are vulnerable to various attacks in these networks. In this paper, we review the network layer attacks and then we simulate the impact of black hole attack on ad hoc on demand...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2016