Parallel Buffer Trees and Searching Cory Fraser School

Parallel Buffer Trees and Searching Cory Fraser School of Computer Science Carleton University, Ottawa, Canada http: //people. scs. carleton. ca/~cfraser 3/ COMP 5704 Project Presentation

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

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. Bn) build time, O(log. Bn) 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. BN/B) I/Os • Parallel B-tree needs O(N/Plog. BN) 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 2 f. B. • 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 f. B 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 <= f. B then remake child nodes. • If > f. B then create new siblings for each f. B/2 operations. Tree rebalancing may be required. COMP 5704 Project Presentation

Node Rebalancing COMP 5704 Project Presentation

Results • 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. 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/2002 F/Uge 11/handbook. pdf • http: //opendatastructures. org COMP 5704 Project Presentation