We have to strike a balance between the security and the computational cost saving using cloud server
5.
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)
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
8.
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
9.
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
10.
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
11.
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
12.
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
13.
Utilization: Shortest Distance Computation
Given a node pair u and v, the shortest distance can be discovered with
…… u v
14.
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.
15.
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
16.
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
17.
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
18.
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
19.
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
20.
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.
21.
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
22.
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.
23.
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
24.
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
25.
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
26.
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
27.
Results related with approximate answers
Scalability
Support large graph
Impact of increase of error bound
Decrease of space cost and time cost in outsourcing
28.
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
29.
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
30.
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