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Sigmod11 outsource shortest path
 

Sigmod11 outsource shortest path

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Sigmod11 outsource shortest path Sigmod11 outsource shortest path Presentation Transcript

  • Neighborhood-Privacy Protected Shortest Distance Computing in Cloud Jun Gao , Jeffrey Yu Xu, Ruoming Jin, Jiashuai Zhou, Tengjiao Wang, Dongqing Yang 14 Jun, 2011, Greece, SIGMOD 2012
  • Outline
    • Motivation
    • Related work
    • Our solution
      • 1-neighborhood-d-radius graph
      • Graph transformation with exact answer
      • Graph transformation with approximate answer
    • Experiment
    • Conclusion & Future work
  • Graph data management in cloud Co a uthor Network , from manyeyes.alphaworks.ibm.com
    • Graph data applications
      • Social network, knowledge network...
    • Time consuming graph operations
      • The shortest distance computing takes O(n 2 )
      • The breadth-first-search requires O(n+m)
      • ......
    Cloud Computing
    • Advantage of cloud computing
      • High computational power
      • Easy maintenance
      • Easy re-provisioning of resources
      • ……
    Can we use the cloud serve to manage graph data , such as to answer shortest distance ?
  • Security issues in graph outsourcing
    • Attacks on outsourced graph
      • Structural Pattern Attack
        • Use sub-graph to re-identify the target part
      • Reconstruction Attack
        • Recover the original graph from outsourced one.
    • Security leakage
      • Regulation of sensitive data violated
      • Untrusted answers produced by cloud server
    We have to strike a balance between the security and the computational cost saving using cloud server
  • Framework of graph outsourcing
    • A reasonable security model on outsourced graph
    • An efficient method to transform the original graph into the outsourced graph
    • (3) An approach to rewrite the query and combine the results
    Client Side Original Graph Graph Transformation Link graph Results Result Combination Cloud Server Outsourced Graph Query Evaluation Query Rewriting Query (2) (1) (3)
  • Outline
    • Motivation
    • Related work
    • Our solution
      • 1-neighborhood-d-radius graph
      • Graph transformation with exact answer
      • Graph transformation with approximate answer
    • Experiment
    • Conclusion & Future work
  • Structural Anonymization
      • Structural anonymization in publishing
        • 1-neighborhood [icde 08], k-degree [sigmod08], k-automorphism [vldb 09], k- isomorphism [sigmod10], etc
        • Using the least amount of modifications of the original graph
    Original graph 4-isomorphism Attacker’s query find 4 sub-graphs No shortest distance preservation No consideration of edge weight
  • Feature preservation graph transformation
    • Eigenvalue preservation [sdm 08]
      • Random add/remove/switch edges
      • Theoretically prove that the eigenvalue can be preserved.
    • Shortest path preservation [icde 10]
      • Express the shortest path preservation by inequality rules
      • Use line programming to find a solution to such rules
      • Requires O(dn 2 ) rules in all shortest path preservation
    No support of exact distance computing No explicit security guarantee
  • Shortest distance index
    • Multiple-level index [tkde98]
      • Select nodes to build a higher level graph
      • Exploit the shortest paths at a higher level graph to guide the path searching at a lower level
    • Landmark index [cikm 09, jacm 09]
      • Select landmark nodes and build the shortest path
      • Exploit the triangle inequality rules to estimate the distance
    • 2-HOP index [soda 02]
      • Annotate incoming and outgoing labels on each node
      • Compute the distance between two nodes with the intersection
    No security consideration
  • Outline
    • Motivation
    • Related work
    • Our solution
      • 1-neighborhood-d-radius graph
      • Graph transformation with exact answer
      • Graph transformation with approximate answer
    • Experiment
    • Conclusion & Future work
  • 1- Neighborhood-d-Radius Graph
    • Intuition
      • Protect the neighborhood information and the close relationship between nodes.
    • Privacy protection
      • Find empty meaningful results for any query pattern
    ( 1-neighborhood ): for any node pair u and v ∈ Vo, (u, v) ∉ E ( d-radius ): for any node pair u and v ∈ Vo, δ G (u, v) >= d. Original graph Attacker’s query 2-radius graph
  • 1-Neighborhood-d-Radius Graph too strong?
    • Can we hide the neighbors and relationship with distance less than d, and add direct edges among others?
    • No, using triangle inequality rules will find the “hidden” edges
      • Reconstruction Attack
    Original graph non-2-radius graph
  • Utilization: Shortest Distance Computation
    • Given a node pair u and v, the shortest distance can be discovered with
    …… u v
  • Graph Transformation Problem
    • Given a graph G = (V,E) and d, the graph transformation produces outsourced graphs G o = {G 1, ...G j } , and a local link graph G l, which achieves the following objectives:
      • Security
        • Each outsourced graph is a 1-neighborhood-d-radius graph;
      • Utility
        • The union of G o and G l can answer the shortest distance in the original graph;
      • Local computational cost
        • The space cost of G l and the cost of the shortest distance computation on the client side are minimized.
  • Naive Method
    • Steps
      • Enumerate different forms of the candidate solutions
        • One local link graph and outsourced graphs.
      • Find the one with the minimal space cost of local graph.
    • Searching space
      • The nodes in a outsourced graph are a sub-set of the these in original graph, and the different forms of outsourced graph can be O(2 n )
      • The brute force strategy will lead to exponential time cost
  • Greedy Method
    • Basic idea
      • Generate more “ expressive ” outsourced graph which can answer more shortest paths.
        • Edges in link graph can be reused so that the space cost of link graph is reduced
    • Challenges
      • How to find “expressive” outsourced nodes?
      • How to build d-radius graph from the select nodes?
    • Steps
      • 1. Enumerate all shortest paths, find possible candidate outsourced nodes, and assign benefit on nodes
      • 2. Generate outsourced graphs according to node benefit
  • Step 1: Enumerate shortest path and benefit assignment
    • Candidate outsourced node pair
      • node pair (x,y) can be used to answer shortest distance between (u,v)
      • (x,y) should meet d-radius.
      • x is close to u, y is close to v
    • Benefit function
      • Record the frequency of a node (or node pair) which can be outsourced
  • Step 2: Generate one outsourced graph
    • Node selection
      • The node which is with the next maximal benefit and is not in any cluster, can be selected
      • Build a d-radius cluster for the selected node
    • Edge building
      • The edge weight is the shortest distance between cluster centers
  • Graph transformation with approximate answer
    • Graph transformation with exact answer at least requires enumeration of all shortest paths.
    • Approximate distance can be acceptable in many domains
    • Approximate distance can be measured by
    • Basic idea
      • Transform graph to achieve α = 1 and a given average additive error β ?
    • Main steps
      • Construct outsourced graph in a relaxed way
      • Estimate the average additive error
  • Relaxed outsourced graph construction
    • Select outsourced nodes randomly.
    • Relax edge weight assignment
      • Build k shortest path trees
      • In each tree, link the outsourced node with its lowest ancestor as the edge.
  • Estimation of average additive error
    • The error for distance query (u,v) varies according to whether u and v have been outsourced
    • β can be computed as follows:
      • We estimate the percentage of each category with the random node selection assumption
      • The average additive error can be estimated by sampling
  • Heuristic outsourced node selection
    • Single outsourced graph
      • Degree based construction
        • First select the node with the higher degree
      • Cluster size based construction
        • First select the node with more nodes in its cluster
    • Multiple outsourced graphs
      • Avoid outsourcing the same graph.
  • Outline
    • Motivation
    • Related work
    • Our solution
      • 1-neighborhood-d-radius graph
      • Graph transformation with exact answer
      • Graph transformation with approximate answer
    • Experiment
    • Conclusion & Future work
  • Experiment
    • Measures:
      • transformation time cost
      • space cost of link graph
      • average additive error
      • local overhead ratio=
    • Competitor
      • LP-based Edge weight anonymization in ICDE 2010
    • Datasets:
    Time cost with cloud server Time cost without cloud server
  • Results related with exact answers
    • Scalability
      • Better than LP based method
    • Impact of increase of d
      • Strengthen security of outsourced graphs
      • Increase the transformation time cost, the space cost of the link graph
  • Results related with exact answers (cont.)
    • Benefit function
      • Vertex pair based method works better
    • Local overhead ratio
      • Very low
      • Goes down with the increase of graph size
  • Results related with approximate answers
    • Scalability
      • Support large graph
    • Impact of increase of error bound
      • Decrease of space cost and time cost in outsourcing
  • Results related with approximate answers(cont.)
    • Additive error bound
      • Achieves the given additive error quite well
    • Local overhead ratio
      • Declines with the increase of nodes
  • Outline
    • Motivation
    • Related work
    • Our solution
      • 1-neighborhood-d-radius graph
      • Graph transformation with exact answer
      • Graph transformation with approximate answer
    • Experiment
    • Conclusion & Future work
  • Conclusion & Future work
    • Conclusion:
      • A 1-neighbourhood-d- radius security model
      • A greedy method to transform graph with exact answer
      • A method to transform graph with approximate answer
      • Extensive experimental results on real and synthetic data
    • Future work:
      • More graph operations.
      • Stronger security model
      • Incremental graph outsourcing over dynamic graphs
      • [email_address]