Many of the available RDF datasets describe millions of resources by using billions of triples. Consequently, millions of links can potentially exist among such datasets. While parallel implementations of link discovery approaches have been developed in the past, load balancing approaches for local implementations of link discovery algorithms have been paid little attention to. In this paper, we thus present a novel load balancing technique for link discovery on parallel hardware based on particle-swarm optimization. We combine this approach with the Orchid algorithm for geo-spatial linking and evaluate it on real and artificial datasets. Our evaluation suggests that while naïve approaches can be superlinear on small data sets, our deterministic particle swarm optimization outperforms both naïve and classical load balancing approaches such as greedy load balancing on large datasets.

1. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
DPSO
An Optimization Approach for Load Balancing in Parallel
Link Discovery
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo
September 17, 2015
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 1/30

2. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Outline
1 Motivation
2 Load Balancing Approaches
3 Evaluation
4 Conclusion and Future Work
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 2/30

3. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Outline
1 Motivation
2 Load Balancing Approaches
3 Evaluation
4 Conclusion and Future Work
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 3/30

4. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Link Discovery (LD)
Why LD?
1 Fourth principle
2 Links are central for
Cross-ontology QA
Data Integration
Reasoning
Federated Queries
...
LD Time complexity
Large number of triples (> 63 billion triples)
Quadratic runtime
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 4/30

5. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Load Balancing for LD
Need to develop highly scalable LD algorithms
Local hardware LD
Suffer less from the data transfer bottleneck
Better runtime than parallel LD approaches on remote
hardware (e.g. cloud-based approaches)
Current load balancing approaches for local LD
Paid little attention
Mostly na¨ıve implementations
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 5/30

6. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Load Balancing for LD
Need to develop highly scalable LD algorithms
Local hardware LD
Suffer less from the data transfer bottleneck
Better runtime than parallel LD approaches on remote
hardware (e.g. cloud-based approaches)
Current load balancing approaches for local LD
Paid little attention
Mostly na¨ıve implementations
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 5/30

7. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Load Balancing for LD
Need to develop highly scalable LD algorithms
Local hardware LD
Suffer less from the data transfer bottleneck
Better runtime than parallel LD approaches on remote
hardware (e.g. cloud-based approaches)
Current load balancing approaches for local LD
Paid little attention
Mostly na¨ıve implementations
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 5/30

8. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Load Balancing Problem
Given:
n tasks τ1, ..., τn
Computational complexities c(τ1), ..., c(τn)
m processors
Goal:
Distribute τi across m processors as evenly as possible
Example
3 tasks τ1, τ2 and τ3 with complexities 3, 4 resp. 6
2 processors
An optimal distribution:
P1 → {τ1, τ2}
P2 → {τ3}
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 6/30

9. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Load Balancing Problem
Given:
n tasks τ1, ..., τn
Computational complexities c(τ1), ..., c(τn)
m processors
Goal:
Distribute τi across m processors as evenly as possible
Example
3 tasks τ1, τ2 and τ3 with complexities 3, 4 resp. 6
2 processors
An optimal distribution:
P1 → {τ1, τ2}
P2 → {τ3}
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 6/30

10. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Outline
1 Motivation
2 Load Balancing Approaches
3 Evaluation
4 Conclusion and Future Work
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 7/30

11. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Load Balancing for LD
Notations
Given S, T of source resp. target resources
Divides S, T such that
k
i=1
Si = S and
l
j=1
Tj = T
Determines (Si , Tj ) whose elements are to be compared
The idea of load balancing is to distribute the
computation of Si × Tj over m processors
Task τ: Comparing elements in (Si , Tj )
c(τ) = |Si | · |Tj |
block B: Set of all tasks assigned to a single processor
c(B) =
t∈B
c(τ)
MSE = m
i=1 c(Bi ) − m
j=1
c(Bj )
m
2
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 8/30

12. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Load Balancing for LD
Notations
Given S, T of source resp. target resources
Divides S, T such that
k
i=1
Si = S and
l
j=1
Tj = T
Determines (Si , Tj ) whose elements are to be compared
The idea of load balancing is to distribute the
computation of Si × Tj over m processors
Task τ: Comparing elements in (Si , Tj )
c(τ) = |Si | · |Tj |
block B: Set of all tasks assigned to a single processor
c(B) =
t∈B
c(τ)
MSE = m
i=1 c(Bi ) − m
j=1
c(Bj )
m
2
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 8/30

13. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Load Balancing for LD
Notations
Given S, T of source resp. target resources
Divides S, T such that
k
i=1
Si = S and
l
j=1
Tj = T
Determines (Si , Tj ) whose elements are to be compared
The idea of load balancing is to distribute the
computation of Si × Tj over m processors
Task τ: Comparing elements in (Si , Tj )
c(τ) = |Si | · |Tj |
block B: Set of all tasks assigned to a single processor
c(B) =
t∈B
c(τ)
MSE = m
i=1 c(Bi ) − m
j=1
c(Bj )
m
2
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 8/30

14. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Load Balancing for LD
Notations
Given S, T of source resp. target resources
Divides S, T such that
k
i=1
Si = S and
l
j=1
Tj = T
Determines (Si , Tj ) whose elements are to be compared
The idea of load balancing is to distribute the
computation of Si × Tj over m processors
Task τ: Comparing elements in (Si , Tj )
c(τ) = |Si | · |Tj |
block B: Set of all tasks assigned to a single processor
c(B) =
t∈B
c(τ)
MSE = m
i=1 c(Bi ) − m
j=1
c(Bj )
m
2
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 8/30

15. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Load Balancing for LD
Notations
Given S, T of source resp. target resources
Divides S, T such that
k
i=1
Si = S and
l
j=1
Tj = T
Determines (Si , Tj ) whose elements are to be compared
The idea of load balancing is to distribute the
computation of Si × Tj over m processors
Task τ: Comparing elements in (Si , Tj )
c(τ) = |Si | · |Tj |
block B: Set of all tasks assigned to a single processor
c(B) =
t∈B
c(τ)
MSE = m
i=1 c(Bi ) − m
j=1
c(Bj )
m
2
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 8/30

16. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Load Balancing for LD
Notations
Given S, T of source resp. target resources
Divides S, T such that
k
i=1
Si = S and
l
j=1
Tj = T
Determines (Si , Tj ) whose elements are to be compared
The idea of load balancing is to distribute the
computation of Si × Tj over m processors
Task τ: Comparing elements in (Si , Tj )
c(τ) = |Si | · |Tj |
block B: Set of all tasks assigned to a single processor
c(B) =
t∈B
c(τ)
MSE = m
i=1 c(Bi ) − m
j=1
c(Bj )
m
2
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 8/30

17. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Load Balancing for LD
Notations
Given S, T of source resp. target resources
Divides S, T such that
k
i=1
Si = S and
l
j=1
Tj = T
Determines (Si , Tj ) whose elements are to be compared
The idea of load balancing is to distribute the
computation of Si × Tj over m processors
Task τ: Comparing elements in (Si , Tj )
c(τ) = |Si | · |Tj |
block B: Set of all tasks assigned to a single processor
c(B) =
t∈B
c(τ)
MSE = m
i=1 c(Bi ) − m
j=1
c(Bj )
m
2
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 8/30

18. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Running Example
4 tasks {τ1, τ2, τ3, τ4}
Respective complexities {7, 1, 8, 3}
2 processors P1, P2
Tasks: 7 1 8 3
Processors: 1 1
τ1 assigned to P1: 7
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 9/30

19. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Na¨ıve Load Balancer
Idea
Divides tasks between processors based on their index and
regardless of complexity
Example
Processors assignment: 7 1 8 3 MSE = 30.25
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 10/30

20. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Greedy Load Balancer
Idea
1 Sorts tasks in descending order based on their complexity
2 Starting from the most complex task, assigns tasks to
processors in order
Example
1. Sorted tasks: 8 7 3 1
2. Processors assignment: 8 7 3 1
MSE = 2.25
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 11/30

21. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Pair-Based Load Balancer
Idea
1 Sorts tasks according to task complexity
2 In order, assigns ith
and (n − i + 1)th
tasks to Pi
Example
1. Sort tasks: 1 3 7 8
2. Processors assignment: 1 3 7 8
MSE = 0.25
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 12/30

22. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Particle Swarm Optimization
Idea
Initialization
Best Known Positions (BKP)
BKP ← Partitions the n tasks to m task blocks
Computes fitness function F to the initial BKP
F is the complexity difference between the most and
least loaded blocks
Initializes Best Known Fitness (BKF) to F
Until a termination criterion is met
Performs the particles migration, based on random
particle velocity
Recomputes F
If F < BKF, updates BKF and BKP
Return BKP
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 13/30

23. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Particle Swarm Optimization
Idea
Initialization
Best Known Positions (BKP)
BKP ← Partitions the n tasks to m task blocks
Computes fitness function F to the initial BKP
F is the complexity difference between the most and
least loaded blocks
Initializes Best Known Fitness (BKF) to F
Until a termination criterion is met
Performs the particles migration, based on random
particle velocity
Recomputes F
If F < BKF, updates BKF and BKP
Return BKP
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 13/30

24. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Particle Swarm Optimization
Idea
Initialization
Best Known Positions (BKP)
BKP ← Partitions the n tasks to m task blocks
Computes fitness function F to the initial BKP
F is the complexity difference between the most and
least loaded blocks
Initializes Best Known Fitness (BKF) to F
Until a termination criterion is met
Performs the particles migration, based on random
particle velocity
Recomputes F
If F < BKF, updates BKF and BKP
Return BKP
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 13/30

25. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Particle Swarm Optimization
Idea
Initialization
Best Known Positions (BKP)
BKP ← Partitions the n tasks to m task blocks
Computes fitness function F to the initial BKP
F is the complexity difference between the most and
least loaded blocks
Initializes Best Known Fitness (BKF) to F
Until a termination criterion is met
Performs the particles migration, based on random
particle velocity
Recomputes F
If F < BKF, updates BKF and BKP
Return BKP
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 13/30

26. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Particle Swarm Optimization
Example
Termination criterion: max number of iterations of 1
Initialization:
7 1 8 3 BKF = F = 11
First iteration:
7 1 8 3 F = 5
As F < BKF, updates BKF and PKB
MSE = 6.25
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 14/30

27. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Deterministic PSO (DPSO)
DPSO
PSO is non-deterministic
PSO depends on a random selection of velocity for
moving particles
We propose the Deterministic PSO (DPSO)
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 15/30

28. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Deterministic PSO (DPSO)
Idea
Partitions the n tasks to m task blocks
Until termination criterion is met
Finds the most overloaded block B+ and the least
underloaded block B−
Sorts tasks within B+ based in their complexities
As far as a better balancing between B+ to B− is met
Moves tasks in order from B+
to B−
(task migration)
Computes fitness function as complexity difference
between B+ and B−
Returns best known blocks
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 16/30

29. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Deterministic PSO (DPSO)
Why is DPSO deterministic?
Only moves tasks from B+
to B−
(no random migration)
Sorts B+
tasks before task migration start
Insures optimal load balancing between B+
and B−
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 17/30

30. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Deterministic PSO (DPSO)
Example
Termination criterion: max number of iterations of 1
Initialization:
B+
= 8 7 , B−
= 1 3 F = 11
First iteration:
Sorted B+
= 7 8 , B−
= 1 3
Task migration: B+
= 8 , B−
= 1 3 7 F = 3
MSE = 2.25
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 18/30

31. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Outline
1 Motivation
2 Load Balancing Approaches
3 Evaluation
4 Conclusion and Future Work
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 19/30

32. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Evaluation Setup
Orchid
The parallel task generation was based on Orchid
Orchid partitions the surface of the planet
A task is the comparison of all points in two partitions
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 20/30

33. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Evaluation Setup
Datasets
1 5 synthetic geographic datasets
Polygons’ sizes varied from 1 to 10 points
2 3 real geographic datasets
Nuts
DBpedia
LinkedGeoData
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 21/30

34. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Evaluation Setup
Hardware
64-core server running OpenJDK 64-Bit Server 1.6.0 27
on Ubuntu 12.04.2 LTS.
8 quad-core processor Intel(R) Core(TM) i7-3770 CPU @
3.40 GHz with 8192 KB cache
Each experiment was assigned 20 GB of memory
PSO
PSO ran 5 times in each experiment and provide the
mean of the 5 runs
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 22/30

35. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Orchid vs. Parallel Orchid
Goal
Evaluate the speedup gained by using parallel Orchid
For Nuts, PSO and DPSO up to 3 times faster
For LinkedGeoData, PSO and DPSO up to 10 times faster
2 4 8
Number of threads
0.0
0.1
0.2
0.3
0.4
Time(min.)
Naïve
Greedy
PairBased
PSO
DPSO
Orchid
Nuts runtime
2 4 8
Number of threads
1
10
100
1000
Time(min.)
Naïve
Greedy
PairBased
PSO
DPSO
Orchid
LinkedGeoData runtime
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 23/30

36. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Orchid vs. Parallel Orchid
Goal
PSO and DPSO are capable of achieving superlinear
performance, as processor caches are faster than RAM
Greedy and pair-based fail to achieve even the run time of
the normal Orchid, due to significant sorting time
2 4 8
Number of threads
0.0
0.1
0.2
0.3
0.4
Time(min.)
Naïve
Greedy
PairBased
PSO
DPSO
Orchid
Nuts runtime
2 4 8
Number of threads
1
10
100
1000
Time(min.)
Naïve
Greedy
PairBased
PSO
DPSO
Orchid
LinkedGeoData runtime
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 24/30

37. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Parallel Load balancing Algorithms
Goals
Measure each algorithm runtime
Qualify each algorithm data distribution using MSE
2 4 8
Number of threads
0.0
0.1
0.2
0.3
0.4
Time(min.)
Naïve
Greedy
PairBased
PSO
DPSO
Orchid
Nuts runtime
2 4 8
Number of threads
1010
1011
1012
1013
MSE
Naïve
Greedy
PairBased
PSO
DPSO
Nuts MSE
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 25/30

38. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Parallel Load balancing Algorithms
Goals
Measure each algorithm runtime
Qualify each algorithm data distribution using MSE
2 4 8
Number of threads
0.0
0.1
1.0
10.0
Time(min.)
Naïve
Greedy
PairBased
PSO
DPSO
Orchid
DBpedia runtime
2 4 8
Number of threads
1011
1012
1013
MSE
Naïve
Greedy
PairBased
PSO
DPSO
DBpedia MSE
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 26/30

39. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Parallel Load balancing Algorithms
Goals
Measure each algorithm runtime
Qualify each algorithm data distribution using MSE
2 4 8
Number of threads
1
10
100
1000
Time(min.)
Naïve
Greedy
PairBased
PSO
DPSO
Orchid
LinkedGeoData runtime
2 4 8
Number of threads
1009
1010
1011
MSE
Naïve
Greedy
PairBased
PSO
DPSO
LinkedGeoData MSE
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 27/30

40. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Outline
1 Motivation
2 Load Balancing Approaches
3 Evaluation
4 Conclusion and Future Work
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 28/30

41. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Conclusion and Future Work
Conclusion
Presented load balancing techniques for link discovery
Proposed deterministic PSO (DPSO)
Combined load balancing algorithms with Orchid
Evaluated on real and artificial datasets
Future Work
Enable splitting of one task over multiple processors
Implement a caching techniques
Study the combination of DPSO with other task
generation algorithms
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 29/30

42. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Conclusion and Future Work
Conclusion
Presented load balancing techniques for link discovery
Proposed deterministic PSO (DPSO)
Combined load balancing algorithms with Orchid
Evaluated on real and artificial datasets
Future Work
Enable splitting of one task over multiple processors
Implement a caching techniques
Study the combination of DPSO with other task
generation algorithms
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 29/30

43. Motivation Load Balancing Approaches Evaluation Conclusion and Future Work
Thank You!
Questions?
Mohamed Sherif
Augustusplatz 10
D-04109 Leipzig
sherif@informatik.uni-leipzig.de
http://aksw.org/MohamedSherif
http://aksw.org/Projects/LIMES
#akswgroup
Mohamed Ahmed Sherif and Axel-Cyrille Ngonga Ngomo — DPSO 30/30