Identifying intersections among a set of d-dimensional rectangular regions (d-rectangles) is a common problem in many simulation and modeling applications. Since algorithms for computing intersections over a large number of regions can be computationally demanding, an obvious solution is to take advantage of the multiprocessing capabilities of modern multicore processors. Unfortunately, many solutions employed for the Data Distribution Management service of the High Level Architecture are either inefficient, or can only partially be parallelized. In this paper we propose the Interval Tree Matching (ITM) algorithm for computing intersections among d-rectangles. ITM is based on a simple Interval Tree data structure, and exhibits an embarrassingly parallel structure. We implement the ITM algorithm, and compare its sequential performance with two widely used solutions (brute force and sort-based matching). We also analyze the scalability of ITM on shared-memory multicore processors. The results show that the sequential implementation of ITM is competitive with sort-based matching; moreover, the parallel implementation provides good speedup on multicore processors.

1. A Parallel Data
Distribution Management
Algorithm
Gabriele D’Angelo
<g.dangelo@unibo.it>
http://www.cs.unibo.it/gdangelo/
joint work with:
Moreno Marzolla and Marco Mandrioli
Delft, Netherlands
Distributed Simulation and Real Time Applications (DS-RT), 2013

2. Presentation outline

Data Distribution Management (DDM)

DDM algorithms

Parallel Data Distribution Management

Parallel Matching Algorithms

Interval Tree Matching (ITM)

Experimental Evaluation

Conclusions
A Parallel Data Distribution Management Algoriithm
DS-RT 2013
Gabriele D'Angelo <g.dangelo@unibo.it>
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3. Data Distribution Management (DDM)

DDM services are part of the IEEE 1516 “High Level
Architecture” (HLA) specification

DDM is about forwarding events generated on update
regions to a set of subscription regions

A region is a d-dimensional rectangle (d-rectangle) in a ddimensional routing space

The goal is to find all the couples of update and subscription
regions that overlap

We assume that each region corresponds to a single extent
A Parallel Data Distribution Management Algoriithm
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Gabriele D'Angelo <g.dangelo@unibo.it>
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4. DDM: simple example in 2 dimensions
dimension 2
S1
U1
S3
U2
S2
dimension 1

The problem of identifying whether two d-rectangles intersect
can be reduced to d independent intersection problems among
one-dimensional segments

Two d-rectangles intersect if and only if they intersect
among all their projections
A Parallel Data Distribution Management Algoriithm
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Gabriele D'Angelo <g.dangelo@unibo.it>
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5. DDM algorithms: from simple to complex

No DDM: all updates are broadcasted, the filtering is on
receivers. CONS: communication inefficiency

Region-based matching (Brute Force, BF): it tests all the
subscription-update pairs. CONS: computational inefficiency

Grid-based matching: it partitions the routing space into a
grid of d-dimensional cells and finds matches
CONS:
S1

U1
S3
S2
false positives

which cell size is the best?
U2
A Parallel Data Distribution Management Algoriithm
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6. DDM algorithms: from simple to complex

Sort-Based Matching (SBM): before matching, the extents
are sorted. In this way, the overlaps can be found efficiently.
In many cases SBM does better than grid-based [Raczy et al.
2005].

CONS: are there drawbacks?
Binary partition-based: recursive binary partitioning of the
extents. CONS: (more than) quadratic worst case cost
A Parallel Data Distribution Management Algoriithm
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Gabriele D'Angelo <g.dangelo@unibo.it>
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7. DDM algorithms: from simple to complex

Sort-Based Matching (SBM): before matching, the extents
are sorted. In this way, the overlaps can be found efficiently.
In many cases SBM does better than grid-based [Raczy et al.
2005].

CONS: are there drawbacks?
Binary partition-based: recursive binary partitioning of the
extents. CONS: (more than) quadratic worst case cost

… and so, what's the problem?
A Parallel Data Distribution Management Algoriithm
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Gabriele D'Angelo <g.dangelo@unibo.it>
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8. DDM algorithms: from simple to complex

Sort-Based Matching (SBM): before matching, the extents
are sorted. In this way, the overlaps can be found efficiently.
In many cases SBM does better than grid-based [Raczy et al.
2005].

CONS: are there drawbacks?
Binary partition-based: recursive binary partitioning of the
extents. CONS: (more than) quadratic worst case cost

… and so, what's the problem?

Even smartphones are multi-core and we're still dealing with
sequential algorithms

The future of computing is very likely to be many-core
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Gabriele D'Angelo <g.dangelo@unibo.it>
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9. Parallel Data Distribution Management

Easy solution: each core (or CPU) is responsible of a specific
dimension. The “master” core computes the final result
dimension 2
S1
U1
S3
S2
U2
dimension 1
A Parallel Data Distribution Management Algoriithm
DS-RT 2013
Gabriele D'Angelo <g.dangelo@unibo.it>
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10. Parallel Data Distribution Management

Easy solution: each core (or CPU) is responsible of a specific
dimension. The “master” core computes the final result
dimension 2
S1
U1
S3
core 1 →
result 1
A Parallel Data Distribution Management Algoriithm
S2
U2
dimension 1
DS-RT 2013
Gabriele D'Angelo <g.dangelo@unibo.it>
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11. Parallel Data Distribution Management

Easy solution: each core (or CPU) is responsible of a specific
dimension. The “master” core computes the final result
dimension 2
core 2 →
result 2
S1
U1
S3
core 1 →
result 1
A Parallel Data Distribution Management Algoriithm
S2
U2
dimension 1
DS-RT 2013
Gabriele D'Angelo <g.dangelo@unibo.it>
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12. Parallel Data Distribution Management

Easy solution: each core (or CPU) is responsible of a specific
dimension. The “master” core computes the final result
dimension 2
core 2 →
result 2
S1
∩
core 1 →
core 1 →
U1
S3
result 1
S2
U2
dimension 1
final result
A Parallel Data Distribution Management Algoriithm
DS-RT 2013
Gabriele D'Angelo <g.dangelo@unibo.it>
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13. Parallel Data Distribution Management

Easy solution: each core (or CPU) is responsible of a specific
dimension. The “master” core computes the final result

PRO: it can be applied to every DDM algorithm

CONS: what if the number of cores/CPUs is larger
than the number of dimensions?
This solution is not adequate for “many core” environments
We need parallel matching algorithms
A Parallel Data Distribution Management Algoriithm
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Gabriele D'Angelo <g.dangelo@unibo.it>
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14. Parallel matching algorithms

Brute Force (BF): inefficient, embarrassingly parallel

Sort-Based Matching (SBM): efficient, not easy to parallelize

DESIDERATA:

efficient

easy to parallelize

based on a simple data structure

that allows the efficient update/add/delete of extents
(dynamic interval management)
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Gabriele D'Angelo <g.dangelo@unibo.it>
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15. Our proposal: Interval Tree Matching (ITM)

Based on the simple Interval Tree data structure

It can be implemented using priority search trees or
augmented AVL trees. For simplicity we've used the last one
[9, 15]
0 – 19
[1, 13]
0 – 13
[16,18]
11 – 19
interval
[0, 8]
0–8
[2, 7]
2–7
[11, 14]
11 – 14
min lower bound
0
[17, 19]
17 – 19
max upper bound
8
1
13
2
7
9
15
11
14
16
18
17
A Parallel Data Distribution Management Algoriithm
DS-RT 2013
19
Gabriele D'Angelo <g.dangelo@unibo.it>
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16. Our proposal: Interval Tree Matching (ITM)

Based on the simple Interval Tree data structure

It can be implemented using priority search trees or
upper bound of the subtree
augmented AVL trees. For simplicity we've used the last one
maximum value of the
rooted in this node
minimum value of the
[9, 15]
0 – 19
lower bound of the subtree
rooted in this node13]
[1,
0 – 13
[16,18]
11 – 19
interval
[0, 8]
0–8
[2, 7]
2–7
[11, 14]
11 – 14
min lower bound
0
[17, 19]
17 – 19
max upper bound
8
1
13
2
7
9
15
11
14
16
18
17
A Parallel Data Distribution Management Algoriithm
DS-RT 2013
19
Gabriele D'Angelo <g.dangelo@unibo.it>
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17. Our proposal: Interval Tree Matching (ITM)

Based on the simple Interval Tree data structure

It can be implemented using priority search trees or
augmented AVL trees. For simplicity we've used the last one
[9, 15]
0 – 19
balanced tree
[1, 13]
0 – 13
interval
[0, 8]
0–8
insertion and delete
[16,18]
11 – 19
[2, 7]
2–7
[11, 14]
11 – 14
[17, 19]
17 – 19
are efficient
min lower bound
0
max upper bound
8
1
13
2
7
9
15
it contains all the subscription (or the update) regions
11
14
16
18
17
A Parallel Data Distribution Management Algoriithm
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Gabriele D'Angelo <g.dangelo@unibo.it>
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18. Interval Tree Matching (ITM): algorithm description

Support function INTERVAL-QUERY:
returns the list of intervals intersecting a given extent

Main function:
1)
create the Interval Tree with all the subscription extents
2)
for every update extent perform an INTERVAL-QUERY
A Parallel Data Distribution Management Algoriithm
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Gabriele D'Angelo <g.dangelo@unibo.it>
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19. Interval Tree Matching (ITM): comparison

Support function INTERVAL-QUERY:
returns the list of intervals intersecting a given extent

Main function:
1)
create the Interval Tree with all the subscription extents
2)
for every update extent perform an INTERVAL-QUERY
Algorithm
Computational cost
Additional space
O(n·m)
Brute force
with n subscription extents,
none
m update extents
Sort-based
O((n+m)log(n+m)+n·m)
O(n+m)
O(min{n·m, (K+1)log n})
Interval tree
with K ≤ n·m that is the total number of
O(n)
intersections
A Parallel Data Distribution Management Algoriithm
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Gabriele D'Angelo <g.dangelo@unibo.it>
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20. Interval Tree Matching (ITM): comparison

Support function INTERVAL-QUERY:
returns the list of intervals intersecting a given extent

Main function:
1)
create the Interval Tree with all the subscription extents
2)
for every update extent perform an INTERVAL-QUERY
Algorithm
Brute force
Computational cost
Additional space
Parallelization: the queries at
O(n·m)
point 2) are independent → it is
none
with n subscription extents,
trivial to parallelize
m update extents
Sort-based
O((n+m)log(n+m)+n·m)
O(n+m)
O(min{n·m, (K+1)log n})
Interval tree
with K ≤ n·m that is the total number of
O(n)
intersections
A Parallel Data Distribution Management Algoriithm
DS-RT 2013
Gabriele D'Angelo <g.dangelo@unibo.it>
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21. Interval Tree Matching (ITM): comparison

Support function INTERVAL-QUERY:
returns the list of intervals intersecting a given extent

Main function:
1)
create the Interval Tree with all the subscription extents
2)
for every update extent perform an INTERVAL-QUERY
Dynamic interval management:
updates are efficient
Algorithm
Brute force
Computational cost
Additional space
Parallelization: the queries at
O(n·m)
point 2) are independent → it is
none
with n subscription extents,
trivial to parallelize
m update extents
Sort-based
O((n+m)log(n+m)+n·m)
O(n+m)
O(min{n·m, (K+1)log n})
Interval tree
with K ≤ n·m that is the total number of
O(n)
intersections
A Parallel Data Distribution Management Algoriithm
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Gabriele D'Angelo <g.dangelo@unibo.it>
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22. Experimental evaluation

The very same methodology used in [Raczy et al. 2005]

Instances with a single dimension are considered

Main parameters:

= number of extents = [50x103, 500x103] with 50% of update extents


N
α
= overlapping degree =
Execution platform:
∑ area of extents
area of the routing space
= {0.01, 1, 100}
Intel® Core© i7-2600 3.40 GHz CPU with 4 physical
cores and Hyper-Threading (HT), 16 GB RAM, Ubuntu 11.04
A Parallel Data Distribution Management Algoriithm
DS-RT 2013
Gabriele D'Angelo <g.dangelo@unibo.it>
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23. Experimental evaluation

The very same methodology used in [Raczy et al. 2005]

Instances with a single dimension are considered

Main parameters:

= number of extents = [50x103, 500x103] with 50% of update extents


N
α
= overlapping degree =
Execution platform:
∑ area of extents
area of the routing space
= {0.01, 1, 100}
Intel® Core© i7-2600 3.40 GHz CPU with 4 physical
cores and Hyper-Threading (HT), 16 GB RAM, Ubuntu 11.04
All the source code and scripts used for this performance
evaluation are available with a Free Software license from:
http://pads.cs.unibo.it
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24. Experimental evaluation: sequential execution
α=0.01
α=1
α=100

BF is very slow

SBM is unaffected by

ITM has the best performance

Increasing α, the gap between SBM
and ITM decreases

Note that α = 100 is a very high
overlay degree
A Parallel Data Distribution Management Algoriithm
α
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Gabriele D'Angelo <g.dangelo@unibo.it>
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25. Experimental evaluation: parallel execution
A Parallel Data Distribution Management Algoriithm
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Gabriele D'Angelo <g.dangelo@unibo.it>
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26. Experimental evaluation: parallel execution
A Parallel Data Distribution Management Algoriithm
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Gabriele D'Angelo <g.dangelo@unibo.it>
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27. Experimental evaluation: parallel execution
Execution platform with 4
physical cores but with
Hyper-Threading
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28. Experimental evaluation: parallel execution
A Parallel Data Distribution Management Algoriithm
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29. Experimental evaluation: parallel execution
A Parallel Data Distribution Management Algoriithm
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Gabriele D'Angelo <g.dangelo@unibo.it>
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30. Experimental evaluation: parallel execution
BF is embarrassingly parallel, in the range [1, 4] (physical
cores) both algorithms obtain almost the same speedup
A Parallel Data Distribution Management Algoriithm
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Gabriele D'Angelo <g.dangelo@unibo.it>
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31. Experimental evaluation: parallel execution
In the range [5, 8] (Hyper-Threading logical cores) ITM is
better than BF. HT provides a performance boost
A Parallel Data Distribution Management Algoriithm
DS-RT 2013
Gabriele D'Angelo <g.dangelo@unibo.it>
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32. Experimental evaluation: parallel execution
With more threads than logical cores there is a
significant performance drop
A Parallel Data Distribution Management Algoriithm
DS-RT 2013
Gabriele D'Angelo <g.dangelo@unibo.it>
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33. Experimental evaluation: parallel execution
8 threads
As expected, the ITM depends on both the number
of extents and the overlap degree α
A Parallel Data Distribution Management Algoriithm
DS-RT 2013
Gabriele D'Angelo <g.dangelo@unibo.it>
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34. Conclusions

We've proposed a new parallel Data Distribution Management
(DDM) mechanism called Interval Trees Matching (ITM)

Both sequential and parallel implementations of ITM show
good results when compared to the state of the art

Since updates on the interval tree are efficient, the ITM can be
easily extended to deal with the dynamic matching problem

All our source code is available with a Free Software license:
we believe that all the published results have to be
reproducible
A Parallel Data Distribution Management Algoriithm
DS-RT 2013
Gabriele D'Angelo <g.dangelo@unibo.it>
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35. Further information
Moreno Marzolla, Gabriele D'Angelo, Marco Mandrioli
A Parallel Data Distribution Management Algorithm
Proceedings of the 16-th ACM/IEEE International Symposium on Distributed
Simulation and Real Time Applications (DS-RT 2013). Delft, Netherlands, 2013
An draft version of this paper is available on the
open e-print archive
All the source code used in this paper is available at
http://pads.cs.unibo.it
Gabriele D'Angelo

E-mail: <g.dangelo@unibo.it>

http://www.cs.unibo.it/gdangelo/
A Parallel Data Distribution Management Algoriithm
DS-RT 2013
Gabriele D'Angelo <g.dangelo@unibo.it>
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36. A Parallel Data
Distribution Management
Algorithm
Gabriele D’Angelo
<g.dangelo@unibo.it>
http://www.cs.unibo.it/gdangelo/
joint work with:
Moreno Marzolla and Marco Mandrioli
Delft, Netherlands
Distributed Simulation and Real Time Applications (DS-RT), 2013