COMP 5704 Project Presentation Parallel Buffer Trees and Searching Cory Fraser School of Computer Science Carleton University, Ottawa, Canada

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 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 us/articles/download-intel-cilk-sdkhttp://software.intel.com/en- us/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 Results Test System Specs: Quad-core running Fedora 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 L. Arge, External Memory Data Structures - c.dk/research/algorithms/Kurser/AA/2002F/Uge 11/handbook.pdf c.dk/research/algorithms/Kurser/AA/2002F/Uge 11/handbook.pdf