Slides - SNAP - Stanford University

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Search for a key in the network of N nodes visits O(log N) nodes Assume that node n queries for key k Let the key k reside at node t How many steps do we need to reach t? 10/6/2011 Jure Leskovec, <strong>Stanford</strong> CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 60
We start the search at node n Let i be a number such that t is contained in interval [n+2 i-1 , n+2 i ] Then the table at node n contains a pointer to node n+2 i-1 – the smallest node f from the interval Claim: f is closer to t than n So, in one step we halved the distance to t We can do this at most log N times Thus, we find t in O(log N) steps 10/6/2011 Jure Leskovec, <strong>Stanford</strong> CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 61
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CS224W: Social and Information Netw
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(1) What is the structure of a soci
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10/6/2011 Jure Leskovec, Stanford C
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Consequence of expansion: Short pa
Page 9 and 10: Could a network with high clusterin
Page 11 and 12: High clustering High diameter N h =
Page 13 and 14: Alternative formulation of the mode
Page 15 and 16: Could a network with high clusterin
Page 17 and 18: s only knows locations of its frien
Page 19 and 20: Model: 2-dim grid where each node h
Page 21 and 22: Claim: Expected search time is ≥
Page 23 and 24: Claim: Getting from s to t takes
Page 25 and 26: Model [Kleinberg, Nature ‘01] No
Page 27 and 28: We need to calculate: P(v → w) =
Page 29 and 30: We have: I ... interval of d/2 aro
Page 31 and 32: Small α: too many long links Big
Page 33 and 34: h(u,v) = tree-distance (height of t
Page 35: Extension: Multiple hierarchies -
Page 38 and 39: Generalized hierar. model: Arbitra
Page 40 and 41: P(u→v) = rank u(v) -α What is b
Page 42 and 43: Decentralized search in a LiveJourn
Page 44 and 45: Getting close (10km) is very easy.
Page 46: Why is rank exponent close to -1?
Page 49 and 50: 10/6/2011 Jure Leskovec, Stanford C
Page 51 and 52: Napster existed from June ‘99 and
Page 53 and 54: Protocol Chord consistently maps ke
Page 55 and 56: Assume we have N nodes and K keys (
Page 57 and 58: A node maintains a table of m=log(N
Page 59: N42+1 = N48 N42+2 = N48 N42+4 = N48
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Slides - SNAP - Stanford University

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