1. Peer-to-Peer Discovery of Semantic Associations
Matthew Perry, Maciej Janik, Cartic Ramakrishnan, Conrad Ibanez, Budak Arpinar, Amit Sheth
2nd International Workshop on Peer-to-Peer Knowledge Management,
San Diego, California, July 17, 2005

2. Semantic Discovery1 From ….. Finding things To …..
Finding out about things
Relationships! 1.

3. Semantic Associations
Relationship-centric nature of Semantic Web data models
We can ask questions about the relationships between objects
How is entity A related to entity B?
Applications
National Security – Insider Threat1
Improved Searching – Bio Patent Miner2
B. Aleman-Meza, P. Burns, M. Eavenson, D. Palaniswami, A. Sheth, An Ontological Approach to the Document Access Problem of Insider Threat, Proceedings of the IEEE Intl. Conference on Intelligence and Security Informatics (ISI-2005), May 19-20, 2005
Sougata Mukherjea, Bhuvan Bamba, BioPatentMiner: An Information Retrieval System for BioMedical Patents, VLDB 2004.

4. Semantic Associations
Define a set of operators ρ for querying complex relationships between entities (Semantic Associations)1
“Matt”
“Perry”
fname
lname
Semantic Association
name
“The University
of Georgia”
&r1
&r6
worksFor
associatedWith
ρ-path
&r5
name
“LSDIS Lab”
Adapted From: Kemafor Anyanwu, and Amit Sheth, ρ-Queries: Enabling Querying for Semantic Associations on the Semantic Web, The Twelfth International World Wide Web Conference, Budapest, Hungary, pp

5. Uniqueness of Semantic Association Queries
Simple query specification (only the two endpoints)
Doesn’t require extensive knowledge of schema
ρ-path (A, B)

6. Difficult to express with existing Query Languages
SELECT ?startURI, ?property_1, ?endURI
FROM (?startURI ?property_1 ?endURI)
FROM (?endURI ?property_1 ?start)
SELECT ?startURI, ?property_1, ?x, ?property_2, ?endURI
FROM (?startURI ?property_1 ?x)(?x ?property_2 ?endURI)
WHERE ?startURI ne ?x && ?endURI ne ?x
FROM (?startURI ?property_1 ?x)(?endURI ?property_2 ?x)
FROM (?x ?property_1 ?startURI)(?x ?property_2 ?endURI)
FROM (?x ?property_1 ?startURI)(?endURI ?property_2 ?x)
RDQL: Find paths of length at most 2 from startURI to endURI

7. Why Semantic Associations in P2P?
Data on the web by its nature is distributed
Knowledge will be stored in multiple stores and multiple ontologies
Search for semantic paths will have to include many knowledge sources
In the spirit of the Semantic Web (collaborative knowledge discovery)

8. Contributions
Super-Peer Architecture for Querying Semantic Associations
Knowledgebase Borders and Distances between Borders
Query Planning Algorithm based on Knowledgebase Borders and Distances

9. Assumptions
Pair-wise mapping of resources between peers (solution to Entity Disambiguation / Reference Reconciliation problem)
We use URIs to solve Entity Disambiguation problem
Main focus is Query Planning over P2P network
Not concerned with fault tolerance, details of network formation, etc. at this point

10. RDF Instance Graph typeOf(instance) purchased String Passenger Ticket
subClassOf(isA)
fname
for
String
subPropertyOf
lname
forflight
number
String
purchased
paidby no
creditedto
Flight
Bank
Account
String
Customer
RDF Instance Graph
Payment
amount
holder
float
FFlyer
fflierno
FFNo
ffid
String
CCard
Cash
Client
&r4
ffid
“XYZ123”
&r11
holder
fflierno
“John”
fname
purchased
&r2
paidby
&r3
&r1
“Smith”
lname
creditedto
paidby
purchased
“Jeff”
“Brown ”
fname
for
&r5
&r6
lname
“Bill”
“Jones”
fname
paidby
&r7
purchased
&r8
&r9
holder
lname

11. ρ-path Problem (k-hop limited)
Given:
An RDF instance graph G, vertices a and b in G, an integer k
Find:
All simple, undirected paths p, with length less than or equal to k, which connect a and b

12. Distributed ρ-path problem: Find all paths from a start node to an end node over the distributed RDF graphs
Knowledge bases - ontologies

13. What do we need? Efficiently explore node neighborhoods
When to stop a search in one peer and continue it in another
Determine the search distance in each peer
Determine which peers to include in the search

14. Approach Peer KB Peer Peer KB KB Super-Peer subgraph Peer ρ-path
RDF data store (sesame, bhrams)
ρ-path (a, b, k)
returns subgraph
Approach
No data store
Responsible for Query Planning
Peer KB
Peer
Peer KB KB
Super-Peer
Peer
subgraph
ρ-path
ρ-sub-plan
ρ-sub-plan
ρ-plan KB
ρ-path
ρ-sub-plan
ρ-sub-plan
Super-Peer
Peer
Super-Peer KB
Peer
subgraph KB
ρ-path
Peer
ρ-sub-plan
ρ-sub-plan KB
Peer KB
Peer KB
subgraph
ρ-path

15. Knowledgebase Borders
Overlap (Peer_1:Peer_2 Border)
Peer 2
Peer 1
Border Node

16. Distance Between Borders
P1:P2
Peer 2
Peer 1
Border node
Query end point
End
P1:P3
dist (P1:P2, P1:P3) = 3
dist (P1:P2, P2:P3) = 1
Dist (P1:P3, P2:P3) = 1
P2:P3
Peer 3
Start

17. Query Planning Graph Directed Graph Node for each distinct border
For each pair of connected borders, create 2 edges (one in each direction)
Weight is the minimum of the minimum distances (reported by peers)
For example you can get from A:B to A:B:C through either A or B

18. Query Planning Graph A B C 3 AB 2 4 3 ABC 2 3 AC BC 5 2 3
Minimum Distances
dist (AB, BC) = 4
dist (AB, AC) = 3
dist (AB, ABC) = 2
dist (BC, AC) = 5
dist (BC, ABC) = 3
dist (AC, ABC) = 2
dist (AB, BB) = 3
dist (AC, AC) = 3
dist (BC, BC) = 2
dist (ABC, ABC) = ∞
Borders AB AC BC
ABC 4 3
ABC 2 3 AC BC 5 3 2

19. Using the Query Planning Graph
Example Query: r-path (start, end, 10) A
1) Find Start and End Points 2 C 3 2 4
2) Compute Distances to Borders B
end 2 2
start

20. 3) Add this Information to QPGAB 2
start 2 4 3
ABC 2 4
4) Find all paths from start to end (including cycles) <= k (10) 2 3 AC BC 5 2
In this case 22 paths 3 3 2 2
end

21. 5) Convert Set of Paths to Set of Queries
start – 2  Peer_A:Peer_B – 3  Peer_A:Peer_C – 3  end
start – 2  Peer_B:Peer_C – 2  Peer_B:Peer_C – 2  end A 3 3 2 C 2 2 B
end 2
start

22. Converting Paths to Queries2 3
start 3
end
A:B
A:C
Each edge (pair of endpoints) represents a query
For example, ρ-path (start, Peer_A:Peer_B, 2)
What is the correct hop-limit?
hop-limit = edge weight + (k – path weight)
ρ-path (start, Peer_A:Peer_B, 4)
ρ-path (Peer_A:Peer_B, Peer_A:Peer_C, 5)
ρ-path (Peer_A:Peer_C, end, 5)
k = 10

23. Find the maximum hop-limit for each pair of end points
(start, Peer_A:Peer_B) 5
(start, Peer_A:Peer_B:Peer_C) 7
(start, Peer_B:Peer_C) 8
(Peer_A:Peer_B, Peer_A:Peer_C)
(Peer_A:Peer_B, Peer_A:Peer_B:Peer_C)
(Peer_A:Peer_B, Peer_A:Peer_B) 3
(Peer_A:Peer_B, Peer_B:Peer_C) 6
(Peer_A:Peer_C, Peer_A:Peer_B:Peer_C)
(Peer_A:Peer_C, Peer_B:Peer_C)
(Peer_A:Peer_C, end)
(Peer_B:Peer_C, end)
(Peer_B:Peer_C, Peer_B:Peer_C)
(Peer_B:Peer_C, Peer_A:Peer_B:Peer_C)
(Peer_A:Peer_B:Peer_C, end)

24. Which Peer gets each query?
ρ-path (Peer_B:Peer_A, Peer_A:Peer_C, 5)
Peer_A
Peer_A
ρ-path (Peer_B:Peer_C, Peer_B:Peer_C, 5) 5
Peer_B and Peer_C
Peer_C
Peer_B

25. Final Query Plan Queries for Peer_B Queries for Peer_A
FROM: Peer_B:Peer_C TO: Peer_B:Peer_C Hop Limit: 6
FROM: Peer_B:Peer_C TO: start Hop Limit: 8
FROM: Peer_A:Peer_B TO: start Hop Limit: 5
FROM: Peer_A:Peer_B TO: Peer_A:Peer_B:Peer_C Hop Limit: 5
FROM: Peer_A:Peer_B TO: Peer_A:Peer_B Hop Limit: 3
FROM: Peer_A:Peer_B:Peer_C TO: Peer_B:Peer_C Hop Limit: 5
FROM: Peer_A:Peer_B TO: Peer_B:Peer_C Hop Limit: 6
FROM: Peer_A:Peer_B:Peer_C TO: start Hop Limit: 7
Queries for Peer_C
FROM: Peer_B:Peer_C TO: end Hop Limit: 8
FROM: Peer_B:Peer_C TO: Peer_B:Peer_C Hop Limit: 6
FROM: Peer_A:Peer_C TO: Peer_B:Peer_C Hop Limit: 5
FROM: Peer_A:Peer_B:Peer_C TO: end Hop Limit: 6
FROM: Peer_A:Peer_B:Peer_C TO: Peer_A:Peer_C Hop Limit: 3
FROM: Peer_A:Peer_C TO: end Hop Limit: 5
FROM: Peer_A:Peer_B:Peer_C TO: Peer_B:Peer_C Hop Limit: 5
Queries for Peer_A
FROM: Peer_A:Peer_B:Peer_C TO: Peer_A:Peer_C Hop Limit: 3
FROM: Peer_A:Peer_B TO: Peer_A:Peer_C Hop Limit: 5
FROM: Peer_A:Peer_B TO: Peer_A:Peer_B:Peer_C Hop Limit: 5
FROM: Peer_A:Peer_B TO: Peer_A:Peer_B Hop Limit: 3

26. Query Execution at Peer
Input:
Set of Queries: { ρ-path ({uri, …}, {uri, …}, k), …}
Algorithm:
Graph Traversal of Main Memory representation
Bi-directional BFS
Results in a set of statements
Output:
Union of each set of statements

27. Query Execution at Peer
Peer does not enumerate paths
Returns a subgraph (set of triples)
Benefits
Eliminates redundant data transfer
Saves computation time

28. Scalability: Multiple Super-Peers
Super-Peer/Super-Peer Borders
Super-Peer_1:Super-Peer_2
Super-Peer_1:Super-Peer_3
Super-Peer_2:Super-Peer_3
Super-Peer_1
Super-Peer_2
Peer_B
Super-Peer/Peer Borders
Peer_B:Super-Peer_2
Peer_A:Super-Peer_3
Peer_C:Super-Peer_3
Peer_A
Super-Peer_1
Peer_C
Super-Peer_3

29. Integration of SP graph and Peer Graph
Super-Peer_1’s new Peer-Level QPG
A:B 2 4
B:SP2 4
A:SP3 3 3 2 5
A:B:C 3 4
SP1:SP2 2 3 5
A:C
B:C
SP1:SP3 2 2 4
C:SP3

30. Query Planning Algorithm
SP2
SP1 B
start D A C E
end
SP3
1) Find start and end points
2) Compute distances to borders

31. 4
3) Add temporary information for endpoints
(both peer and super-peer QPG)
Super-Peer QPG
SP2:SP3 3 4
4) Find all directed paths <= k connecting
start to end in the Super-Peer QPG 3 6
SP1:SP2
SP1:SP3 2 3 2 6 6
start
end 10
k = 10
start – 6  SP1/SP3 – 2  SP1/SP3 – 2  end
start – 6  SP1/SP3 – 2  end
start – 3  SP1/SP2 – 6  end
start – 10  end

32. 5) Form a list of sub-query-plan requests for each super-peer
FROM: start TO: end Hop-Limit: 10
FROM: start TO: Super-Peer_1:Super-Peer_2 Hop-Limit: 4
FROM: SuperPeer_1:Super-Peer_2 TO: end Hop-Limit: 7
FROM: start TO: Super-Peer_1:Super-Peer_3 Hop-Limit: 8
FROM: Super-Peer_1:Super-Peer_3 TO: Super-Peer_1:Super-Peer_3 Hop-Limit: 2
FROM: Super-Peer_1:Super-Peer_3 TO: end Hop-Limit: 4
Super-Peer_3
FROM: Super-Peer_1:Super-Peer_3 TO: Super-Peer_1:Super-Peer_3 Hop-Limit: 2

33. 7) Each super-peer goes through the previous process on its peer QPG
to form a list of ρ-path queries for its peers
Queries for Peer E:
FROM: E:SP1 TO: E:SP1 Hop Limit: 2
Queries for Peer B:
FROM: A:B TO: A:B Hop Limit: 3
FROM: A:B TO: B:C Hop Limit: 6
FROM: A:B:C TO: B:SP2 Hop Limit: 4
FROM: A:B TO: B:SP2 Hop Limit: 2
FROM: A:SP2 TO: start Hop Limit: 4
FROM: B:C TO: B:SP2 Hop Limit: 5
FROM: B:C TO: start Hop Limit: 8
FROM: B:C TO: B:C Hop Limit: 6
FROM: A:B TO: start Hop Limit: 5
FROM: A:B TO: A:B:C Hop Limit: 5
FROM: A:B:C TO: start Hop Limit: 7
FROM: A:B:C TO: B:C Hop Limit: 5
Queries for Peer A:
FROM: A:B TO: A:B Hop Limit: 3
FROM: A:B:C TO: A:SP3 Hop Limit: 4
FROM: A:B TO: A:SP3 Hop Limit: 6
FROM: A:B TO: A:C Hop Limit: 5
FROM: A:B TO: A:B:C Hop Limit: 5
FROM: A:B:C TO: A:C Hop Limit: 3
FROM: A:C TO: A:SP3 Hop Limit: 3
Queries for Peer C:
FROM: A:B TO: B:C Hop Limit: 5
FROM: A:B TO: end Hop Limit: 5
FROM: A:B:C TO: end Hop Limit: 6
FROM: B:C TO: end Hop Limit: 8
FROM: B:C TO: B:C Hop Limit: 6
FROM: B:C TO: C:SP3 Hop Limit: 6
FROM: A:C TO: C:SP3 Hop Limit: 3
FROM: A:B:C TO: A:C Hop Limit: 3
FROM: A:B:C TO: B:C Hop Limit: 5
FROM: A:B:C TO: C:SP3 Hop Limit: 4
FROM: C:SP3 TO: end Hop Limit: 4
8) Querying peer now communicates directly with other peers to execute
the ρ-path queries

34. Conclusions and Future Work
Presented a Query-Planning Algorithm for r-path queries over distributed data set
Problems
Efficiently compute node neighborhoods
How to continue searches across KBs
How to check for the many possible cases
How to determine search length in each KB

35. Conclusions and Future Work
Performance Testing
Effect of relative border size
Different criteria for group formation
How to accommodate other types of queries

36. Questions?

37. Computing Borders Super-Peer maintains Sorted Map of URIs Peer Border
Traverse new list and update Sorted Map
Super Peer Border
Don’t care about other URIs not in this group
Keep total data transferred at a minimum

38. Forming the Network I want to join the network 1) Broadcast
3) List of URIs
1) Broadcast
SP2
P New
SP1
SP3 P2 P1
2) I am a super-peer

39. Forming the Network 6) New peer picks one super-peer reject SP2 accept
P New
SP1
SP3
reject P2 P1
4) SPs compute overlap
O(n log k) (maintain
border information)
5) Send overlap count to
new peer

40. Forming the Network 10) Peers send minimum distances SP2 P New SP1 SP3
9) Here are your borders
8) SP1 recomputes SP
borders
7) SP1 updates permanent
uri index

41. Computing Super-Peer Borders
SP1
SP2 C E L M U A B G J S
(SP1, K, false)
(SP1, H, false)
(SP1, C, false)
(SP1, U, true) H H K K H H
(SP2, G, false)
(SP2, null, null)
(SP2, J, true)
(SP2, R, true) K K R R R R

42. Super-Peer Level QPG A B C Super-Peer 1 Super- Peer 3 Super- Peer 2
Borders AB AC BC
A/SP3
B/SP2
C/SP3
Minimum Distances
dist (AB, BC) = 4
dist (AB, AC) = 3
dist (AB, ABC) = 2
dist (BC, AC) = 5
dist (BC, ABC) = 3
dist (AC, ABC) = 2
dist (AC, A/SP3) = 3
dist (AB, A/SP3) = 4
dist (ABC, A/SP3) = 3
dist (AC, C/SP3) = 2
dist (BC, C/SP3) = 4
dist (ABC, C/SP3) = 2
dist (AB, B/SP2) = 2
dist (BC, B/SP2) = 2
dist (ABC, B/SP2) = 2
Super-Peer 1 A B C
Super-
Peer 3
Super-
Peer 2