Zhuo Peng, Chaokun Wang, Lu Han, Jingchao Hao and Yiyuan Ba Proceedings of the Third International Conference on Emerging Databases, Incheon, Korea (August 2011)

  Introduction  Related Work  Preliminary  Algorithm  Experiments  Conclusion Outline 2

  Introduction  Related Work  Preliminary  Algorithm  Experiments  Conclusion Outline 3

  Purpose: to find the most potential stars in social networks to be promoted  How to measure the importance  incoming edge and outgoing edge  most potential stars = minimum promotion cost  How to find the most potential stars  Skyline query  promote a non-skyline member into skyline by adding new edges which are directly connected to it  it will take some costs to add a new edge 4 Introduction

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  member promotion in SNs = to identify the most appropriate non-skyline member(s) which can be promoted to be skyline member(s) by adding edges at minimum cost  To the best of our knowledge, our paper is the first one that raises the member promotion problem in SNs. 6 Problem Definition

  first one that raises the member promotion problem in SNs and provides the formal definition  propose the general promotion algorithmic framework and bring forward the brute-force method for promotion to solve the problem intuitively  utilize several optimization strategies to improve the efficiency and accordingly propose the IDP algorithm  Extensive experiments were conducted to show the effectiveness and efficiency of the IDP algorithm on both real and synthetic datasets 7 Contributions

  Introduction  Related Work  Skyline Query  Skyline Minimum Vector  Preliminary  Algorithm  Experiments  Conclusion Outline 8

  retrieves a subset of data points that are not dominated by any other points in a set of D- dimensional data points  algorithms  Block Nested Loop (BNL)  Divide-and-Conquer (D&C)  Bitmap method  Nearest Neighbor (NN)  Branched and Bound Skyline(BBS) 9 Skyline Query

  studies the query for the points that can be changed to be a skyline point at the minimum cost  The costs are measured by L1 distance of the skyline vectors starting from the original position and pointing to a skyline position. The skyline minimum vector thus indicates minimum L1 distance.  Those non-skyline points which can be changed to be skyline points by the skyline minimum vectors are the solutions to the problem.  Drawbacks  the virtual points which are needed for the computation of the skyline vectors must be provided in advance  the skip region for optimization is not good enough  no theoretical analysis such as time complexity analysis and correctness proof has been provided 10 Skyline Minimum Vector

  Introduction  Related Work  Preliminary  Algorithm  Experiments  Conclusion Outline 11

  An SN is modeled as a directed graph G ( V, E, W )  V = the members in the SN  E = the existing directed edges  Each w ∈ W : V × V → R+ denotes the cost for establishing the edge between any two different members 12 Preliminary

  An SN is modeled as a directed graph G ( V, E, W )  V = the members in the SN  E = the existing directed edges  Each w ∈ W : V × V → R+ denotes the cost for establishing the edge between any two different members 13 Preliminary

  Authoritativeness  Given a node v in an SN G(V, E, W), the authoritativeness of v is denoted as the indegree of v, namely d in (v)  Shows how much attention v can get  Hubness  Given a node v in an SN G(V, E, W), the hubness of v is denoted as the outdegree of v, namely d out (v)  Shows how the importance of v as a hub 14 Authoritativeness and Hubness

  Candidate Set  Given an SN G(V, E, W), let the skyline member set be S G, when S G ≠ V, the set V-S G, denoted as C *, is the candidate set of G. We say each node c ∈ V-S G is a candidate for member promotion  Dominator Set  Given a member v in an SN G(V, E, W), the dominator set of v, marked as δ (v), is defined as a set of nodes D: {n | n dominates v, n ∈ V}. 15 Candidate Set and Dominator Set

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  Given an SN G(V, E, W), ∀ c ∈ C*, p ⊆ V × V, a promotion plan against c, denoted as p, is defined as such an edge combination that satisfies:  (1) p ⊆ {e | e = (c, ·) ∨ e = (·, c) ∧ e ≠ (c, c) ∧ e ∉ E},  (2) c ∉ S G’, where G’ = (V, E + p, W).  In more general cases, the one which only meets (1) is defined as a plan 17 Promotion

  Given an SN G(V, E, W), the cost of any plan p, marked as γ (p), is the sum of the weights corresponding to the edges included in p. As we mark the weight of an edge e as (e), that is, γ (p) = Σ e ∈ p((e)) = Σ e ∈ p (W[e.f rom][e.to])  in which e.from and e.to represent the source node and the sink node of edge e respectively. Thereby, ∀ c ∈ C*, p ∈ Pc, the promotion cost of c is the minimum cost among all the promotion plans. We mark it as ζ (c), namely, ζ (c) = min p ∈ Pc ( γ (p)) 18 Promotion Cost

  Member Promotion in SNs  Given an SN G(V, E, W), member promotion in SNs is to find such a member set R which satisfies: (1) R ⊆ C*, (2) R = {r | r = argmin( ζ (c))} 19 Problem Statement

  Introduction  Related Work  Preliminary  Algorithm  Experiments  Conclusion Outline 20

  A general framework for promotion algorithms  A brute-force method  An index-based dynamic pruning method 21 Algorithm

 1.Offline calculation of the distribution of both measures of all the members 2.Determine the candidate set by skyline query 3.Against each candidate, perform promotions by adding edges in the promotion plans and update the minimum promotion cost if necessary 4.Return the optimal candidate and related optimal promotion plans 22 General Framework

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  Verifies all the possible plans with i edges against all the candidates before we locate the best candidate 24 Brute-Force Algorithm

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  A number of “meaningless” promotions will decrease the efficiency, so we should find a way to recognize the skippable plans for pruning  There are some related theorems and lemmas 26 IDP : The Index-based Dynamic Pruning Algorithm

  Given an SN G(V, E, W), if adding an edge e connecting node v i and the candidate node c still cannot promote c into the skyline set, all the attempts of adding an edge e′ connecting the node v j and c with the same direction as e are not able to successfully promote c, where v j ∈ δ (v i ) 27 IDP : Theorem

 28 IDP : Lemma

  Skyline may change after applying a plan, thus the candidate may still be dominated by other members  In the brute-force algorithm is to recalculate the skyline set based on the whole updated network  Theorem  Given a plan p, let M be the set of members relevant to the edges in p except the candidate c. If a member v neither dominates c before the promotion nor belongs to M, v will still not dominate c after p is conducted. 29 Final Verification

  Just need to eliminate the possibility of any member being a dominator of the candidate c to make sure c is successfully promoted  Two cases  the members connected to any edge in the plan may become new dominators of c because at least one of their two measures will increase after the promotion  the members in the skyline member set may still dominate c 30 Final Verification

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  Introduction  Related Work  Preliminary  Algorithm  Experiments  Conclusion Outline 32

  Implemented using Java with JDK version 1.6.0_10, Inter Core2 Duo CPU T GHz, 1G memory, 120G hard disk, Running Windows XP  Datasets  USAir  Includes 332 nodes and 2126 edges  Power-law set  Used a graph data generator gengraph_win to generate graph datasets 33 Experimental Settings

  we verified the effectiveness by comparing the promotion costs between the IDP algorithm and a random promotion algorithm 34 Comparison on Promotion Cost

  to compare the time cost of the brute-force algorithm and the IDP algorithm on both USAir and Power-law Set respectively 35 Comparison on Time Cost

  Introduction  Related Work  Preliminary  Algorithm  Experiments  Conclusion Outline 36

  Raised a new interesting problem, namely member promotion in in social networks  Purpose two algorithms  the brute-force algorithm  the IDP algorithm  The future work  Further improve the algorithm  Allows several members to promote concurrently 37 Conclusion