Parallel Buffer Trees and
Searching
Cory Fraser
School of Computer Science
Carleton University, Ottawa, Canada http://people.scs.carleton.ca/~cfraser3/
COMP 5704 Project Presentation

• Computational Model
• Parallel Buffer Trees
• Implementation
• Results
COMP 5704 Project Presentation
Outline

Computational Model
• Sequential Buffer Tree operated in the External
Memory Model.
• Minimizes transfers from hard disk -> RAM.
• Parallel Buffer Tree operates in the Parallel
External Memory Model.
• Minimizes transfers from RAM -> CPU cache.
COMP 5704 Project Presentation

Related Search Data Structures
• Binary Search Trees
• Usually analyzed in RAM/PRAM model.
• O(nlogn) build time, O(logn) operation time.
• B-trees
• Analyzed in EM / PEM model.
• O(nlog
B n) build time, O(log
B n) operation time.
• Buffer Tree has O((n/B) log
B
(n/B)) build time.
COMP 5704 Project Presentation

What is a Parallel Buffer Tree?
• An offline data structure.
• An (a,b)-tree variant.
• Performs tree operations in batches to reduce
I/Os.
• Good when there’s a continual large flow of operations to execute.
COMP 5704 Project Presentation

Parallel Buffer Tree Complexity
• For sequences of N insert/delete/find(/range) operations:
• O(sort
P
(N)) I/Os without range search
• O(sort
P
(N) + K/PB) I/Os with range searches.
• sort
P
(N) = O(N/PB log
B
N/B) I/Os
• Parallel B-tree needs O(N/Plog
B
N) I/Os.
COMP 5704 Project Presentation

Required Parallel Algorithms
• Parallel sorting for batch operations.
• Parallel merge sort used.
• Parallel prefix sums
• Needed for range query support.
• Distributes batched operations in buckets.
COMP 5704 Project Presentation

Implementation Overview
• Intel Cilk++ SDK with GCC used.
• Available at http://software.intel.com/enus/articles/download-intel-cilk-sdk
• Parallel merge sort from class used.
• Range query extension not implemented.
COMP 5704 Project Presentation

Implementation Details
• Buffer tree is an (a,b)-tree, a=f/4, b=f, f>= PB
• Each leaf stores up to B elements.
• Each non-leaf has a buffer of size 2fB.
• Internal nodes have k-1 routing elements to direct values to children. k = num. of children
COMP 5704 Project Presentation

Implementation Details - Operations
• Tree builds up batches of PB operations before executing them.
• An operation is its type, value, and timestamp.
• The PB batches operations are split into P blocks and sent to the root in parallel.
COMP 5704 Project Presentation

Emptying Non-fringe buffers
• Sort the buffer by value and timestamp.
• Answer Find operations with matching Insert/Delete operations.
• Cancel out matching Insert/Deleting operations.
• Distribute buffer elements to children based on the routing elements.
• Recursively empty children buffers with more than fB operations.
COMP 5704 Project Presentation

Emptying Fringe Buffers
• Convert all values within children nodes into insert operations with negative infinity timestamp.
• Sort the buffer by value and timestamp.
• Answer Find operations, cancel out
Insert/Deletes.
• Based on remaining operations:
• If <= fB then remake child nodes.
• If > fB then create new siblings for each fB/2 operations.
Tree rebalancing may be required.
COMP 5704 Project Presentation

Node Rebalancing
COMP 5704 Project Presentation

• Test System Specs:
• Quad-core running Fedora 16.
• 12 GB of RAM.
• Sequential comparison structures:
• C++ std::set
• online structure
• Parallel Buffer Tree with 1 worker.
Results
COMP 5704 Project Presentation

Results So Far – Build Times
COMP 5704 Project Presentation

Conclusions
• Parallel speedup vs sequential version is high with enough input.
• Performance is not competitive against equivalent online data structures thus far.
• Would need about 12 cores to match std::set.
• May be practical for high volume external memory applications.
COMP 5704 Project Presentation

Questions
• What is an offline data structure?
• What kind of I/O operations is the Parallel
External Memory (PEM) model concerned with?
• Why can a Buffer tree be loaded with N elements faster than a B-tree according to big-
O?
COMP 5704 Project Presentation

References
• N. Sitchinava, N. Zeh, A Parallel Buffer Tree http://dl.acm.org/citation.cfm?id=2312046
• L. Arge, External Memory Data Structures http://www.itc.dk/research/algorithms/Kurser/AA/2002F/Uge
11/handbook.pdf
• http://opendatastructures.org
COMP 5704 Project Presentation