Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Journal of Algorithms
Computer Architecture, Fourth Edition: A Quantitative Approach
Computer Architecture, Fourth Edition: A Quantitative Approach
DISC '08 Proceedings of the 22nd international symposium on Distributed Computing
CUDA by Example: An Introduction to General-Purpose GPU Programming
CUDA by Example: An Introduction to General-Purpose GPU Programming
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Currently, BDD packages such as CUDD depend on chained hash tables. Although they are efficient in terms of memory usage, they exhibit poor cache performance due to dynamic allocation and indirections of data. Moreover, they are less appealing for concurrent environments as they need thread-safe garbage collectors. Furthermore, to take advantage of the benefits from multi-core platforms, it is best to re-engineer the underlying algorithms, such as whether traditional depth-first search (DFS) construction, breadth-first search (BFS) construction, or a hybrid BFS with DFS would be best. In this paper, we introduce a novel BDD package friendly to multicore platforms that builds on a number of heuristics. Firstly, we re-structure the Unique Table (UT) using a concurrency-friendly Hopscotch hashing to improve caching performance. Secondly, we re-engineer the BFS Queues with hopscotch hashing. Thirdly, we propose a novel technique to utilize BFS Queues to simultaneously work as a Computed Table (CT). Finally, we propose a novel incremental Mark-Sweep Garbage Collector (GC). We report results for both BFS and hybrid BFS-DFS construction methods. With these techniques, even with a single-threaded BDD, we were able to achieve a speedup of up to 8x compared to a conventional single-threaded CUDD package. When two-threads are launched, another 1.5x speedup is obtained.