Efficient Branch and Bound on FPGAs Using Work Stealing and Instance-Specific Designs

Abstract

Branch and bound (B8B) algorithms structure the search space as a tree and eliminate infeasible solutions early by pruning subtrees that cannot lead to a valid or optimal solution. Custom hardware designs significantly accelerate the execution of these algorithms. In this article, we demonstrate a high-performance B8B implementation on FPGAs. First, we identify general elements of B8B algorithms and describe their implementation as a finite state machine. Then, we introduce workers that autonomously cooperate using work stealing to allow parallel execution and full utilization of the target FPGA. Finally, we explore advantages of instance-specific designs that target a specific problem instance to improve performance. We evaluate our concepts by applying them to a branch and bound problem, the reconstruction of corrupted AES keys obtained from cold-boot attacks. The evaluation shows that our work stealing approach is scalable with the available resources and provides speedups proportional to the number of workers. Instance-specific designs allow us to achieve an overall speedup of 47 × compared to the fastest implementation of AES key reconstruction so far. Finally, we demonstrate how instance-specific designs can be generated just-in-time such that the provided speedups outweigh the additional time required for design synthesis.

Hybrid multi-core CPU and GPU-based B&B approaches for the blocking job shop scheduling problem

“…In [23], the authors proposed a parallel B&B algorithm exploiting the advantage of instance specific computing on Field Programmable Gate Array (FPGA) which has proven to be highly efficient in term of area, energy consumption, and performance. In addition, the proposed parallelization is based on work stealing strategies to ensure dynamic load-balancing between the parallel threads.…”