A Parallel Searching Scheme for Multiprocessor Systems and Its Application to Combinatorial Problems

In this paper, we propose a parallelized computational scheme called Parallelized Depth-First Algorithm (PDFA) for Branch-and-Bound (B&B) method that works on multiprocessor systems. It is shown theoretically that the space requirement of PDFA on p processing units is at most p times as much as that of the sequential B&B algorithm with the depth-first search function. Moreover, from our experimental results through simulation, it is known that the computation time of PDFA on p processing units can be resuced to less than 1/p that of the sequential B&B algorithm with the depth-first search function. We name this reduction effect in the computation time Acceleration Effect.