1. Load Balancing and Accelerating Parallel Spatial Join Operations using Bitmap Indexing
Sameh Shohdy, Yu Su, and Gagan Agrawal
Computer Science and Engineering,
The Ohio State University, Columbus, OH
HiPC15 (Bengaluru, India) ,

2. Introduction
Proliferation of spatial data in a variety of spatial-based applications.
Common spatial queries:
Range Queries.
Nearest Neighbor Queries (NN).
Spatial Join Queries (SJ).
This work focuses on Spatial Join queries
This work aims at improving existing sequential and parallel algorithms using Bitmap indexing.

3. Background
Spatial Join: combines two spatial datasets to find pairs of spatial objects that satisfy a certain spatial relation.
Examples:
Find all the cities that exist in Ohio State?
Ohio (State) contains Columbus, Cleveland, Dayton , …etc. (Cities).
Find all the Interstate Highways that intersected with I-70 in Ohio
I-70 intersects with I-71, I-75, and I-77 in Columbus.

4. Background (2) Existing SJ algorithms are divided into:
In-memory SJ algorithms:
Examples: Nested-loop join, indexed nested-loop join, R-Tree, and Plane Sweep,
Perform two passes through both datasets (Filter and Refine) to find related objects.
Filter: represents the objects by their Minimum Bounding Rectangles (MBR) and select a set of candidates to reduce the complexity of the join operation.
Refine: Uses the full representation to evaluate the candidates
Disk-based SJ algorithms:
Examples: Partition based Spatial-Merge join (PBSM) and Size Separation Spatial join (S3).

5. Partition based Spatial-Merge join (PBSM)
Dividing the spatial space into a set of partitions.
Each partition contains a small set of spatial objects from both datasets.
Objects in each partition can be joined using any existing in-memory join algorithms.

6. Challenge
Data skew negatively impact the performance of such partitioning algorithms
Load variation - parallel PBSM join algorithm with 64 cores.

7. Contributions
We describe and effective approach for load-balancing based on Bitmap indexing as a summary of the data, Bitmap Partitioning-based Spatial Join (BPSJ).
We also use bitmaps to speedup in-memory spatial join operation, In-memory Bitmap-based Spatial Join(IBSJ).
Our BPSJ algorithm outperforms parallel well-known PBSM method by an average of 6.1x while IBSJ has an average speed-up of 4.2 times over plane-sweep and times over R-tree method.

8. Bitmap Indexing
att0
Bitmap Vectors 3 4 6 R0 1 R1 R2 R3 R4 V0 V1 V2 V3
A set of bitmap vectors are built without re- organizing the data.
Depends on light processing logic operations (AND, OR, and NOT)
att0
att1 R0 1 R1 3 R2 4 2 R3 6 5 R4
att1
Bitmap Vectors 1 2 5 R0 R1 R2 R3 R4 V0 V1 V2 V3

9. Bitmap Partitioning-based Spatial Join (BPSJ)
Depends on bitmap to efficiently divides the spatial spaces into a set of partitions.
Using pre-generated bitmap vectors,
The actual number of objects per partition can be calculated
Split line can be determined.
A set of splits are generated for each dimension.

10. Example Bitmap indexing of attribute minx in ds1
Bitmap indexing of attribute maxx in ds1
Example
Obj
Maxx
Bitmap Vectors 2 4 5 7 1 3 6 8
<4
>=2
AND
(7 objects)
An example of spatial dataset query processing in X-dimension.

11. In-memory Bitmap-based Spatial Join (IBSJ)
We uses Filter and Refine steps as most of existing in- memory spatial join methods.
Using objects’ MBR, a set of bitmap indexing vectors are generated for Max and Min values in each dimension.
Based-on the spatial relation, the join operation can be performed using only the index vectors.
Example (Intersection):

12. Fixed-precision Approximation Technique

13. Experiments
All experiments have been performed on the RI Cluster from CSE department at The Ohio State University.
Datasets:
Synthetic datasets: We use Spatial Index Library (SaIL) library to generate a uniform and Gaussian distribution datasets.
Real datasets: TIGER/LINE geographical data (US Census Bureau, 2014)
Dataset
Geometry
Number of Objects
ROAD
Polyline
ZIPCODE
Polygon
33144
RAIL
182965

14. Performance of Parallel BPSJ Algorithm

15. Results (Contd)

16. In-memory IBSJ Algorithm Evaluation (Uniform Distribution)

17. In-memory IBSJ Algorithm Evaluation (Gaussian Distribution)

18. In-memory IBSJ Algorithm Evaluation (Real Datasets)

19. Index Size Comparison Dataset DS Size R-Tree Index Bitmap Index ROADMB MB MB
ZIPCODE
1.61MB
1.89 MB
1.55 MB
RAIL
9.03 MB
10.2 MB
2.21 MB

20. Conclusion
This work focuses on improving spatial Join Operation using bitmap index.
We have developed two algorithms , BPSJ for large datasets that cannot fit any memory and in-memory algorithm IBSJ.
IBSJ has an average speedup of 4.2 times over Plane- Sweep and 3.06x over R-tree method.
BPSJ method has a speed-up of 6.1x over PBSM partitioning algorithm.