Lecture 7 - Search on Networks - Navigation and We

Lecture 7 - Search on Networks - Navigation and We -...

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6.207/14.15: Networks Lecture 7: Search on Networks: Navigation and Web Search Daron Acemoglu and Asu Ozdaglar MIT September 30, 2009 1
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Networks: Lecture 7 Outline Navigation (or decentralized search) in networks Web search Hubs and authorities: HITS algorithm PageRank algorithm Reading: EK, Chapter 20.3-20.6 (navigation) EK, Chapter 14 (web search) ( Optional reading: ) “The Small-World Phenomenon: An Algorithmic Perspective,” by Jon Kleinberg, in Proc. of ACM Symposium on Theory of Computing, pp./ 163-170, 2000. 2
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Networks: Lecture 7 Introduction We have studied random graph models of network structure. Static random graph models (Erd¨os-Renyi model, configuration model, small-world model) Dynamic random graph models (preferential attachment model) In the next two lectures, we will study processes taking place on networks. In particular, we will focus on: Navigation or decentralized search in networks Web search: ranking web pages Spread of epidemics 3
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Networks: Lecture 7 Decentralized Search Recall Milgram’s small-world experiment, where the goal was to find short chains of acquaintances (short paths) linking arbitrary pairs of people in the US. A source person in Nebraska is asked to deliver a letter to a target person in Massachusetts. This will be done through a chain where each person forwards the letter to someone he knows on a first-name basis. Over many trials, the average number of intermediate steps in successful chains was found to lie between 5 and 6, leading to six degrees of separation principle. Milgram’s experiment has two fundamentally surprising discoveries. First is that such short paths exist in networks of acquaintances. The small-world model proposed by Watts and Strogatz (WS) was aimed at capturing two fundamental properties of networks: short paths and high clustering. 4
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Networks: Lecture 7 Decentralized Search Second, people are able to find the short paths to the designated target with only local information about the network. If everybody knows the global network structure or if we can “flood the network” (i.e., everyone will send the letter to all their friends), we would be able to find the short paths efficiently. With local information, even if the social network has short paths, it is not clear that such decentralized search will be able to find them efficiently. Figure: In myopic search, the current message-holder chooses the contact that is closest to the target and forwards the message to it. 5
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Networks: Lecture 7 A Model for Decentralized Search—1 Kleinberg introduces a simple framework that encapsulates the paradigm of WS – rich in local connections with a few long range links. The starting point is an n × n two-dimensional grid with directed edges (instead of an undirected ring).
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This note was uploaded on 04/17/2011 for the course ECONOMICS 14.14 taught by Professor Daronacemoglu during the Spring '11 term at MIT.

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Lecture 7 - Search on Networks - Navigation and We -...

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