4.2 Control Process 4.1 Actor Process

(e. g. the Traveling Salesperson Problem), we made the same experiments and enlarged each message to 10000 bytes by sending some additional dummy messages. Since the number of migrated messages for our algorithm is very low in comparison to randomized load balancing methods, we could achieve nearly the same results on all De Bruijn networks. For example, we achieved a speedup of 61.46 on a 64 processor network. 6 Conclusion We presented a universal load balancing strategy for the solution of any branch & bound problem on a distributed system. The experiments show that this strategy works well on networks of up to 256 processors and on networks with very large diameter. So it can be concluded that this strategy will also work on even larger networks. The most interesting fact is that these speedup values were achieved, although, the time of the whole parallel computation was very short, e. g. a speedup of 237.33 on a 256 node network in 138.30 seconds. We claim that most other best rst branch & bound problem can be parallelized with nearly the same eeciency, since we demonstrated that also for larger message sizes this method achieves good speedup values. On the other side, many eecient branch & bound algorithms gain their eeciency by a sophisticated branching method, which uses much longer computation times for each node in the solution tree. In this case the speedup of our algorithm cannot decrease since the communication time is constant and the local computation time of the sequential and parallel algorithm will increase, which leads in general to a better speedup. The presented load balancing algorithm was shown to be best suited for distributed best rst branch & bound algorithms. Since it is not tailored to this application, it can also be applied to other problems. In fact, it is already applied to a distributed at concurrent prolog interpreter 6]. The rst results were encouraging, since the here presented strategy behaves in most cases superior to some other used load balancing algorithms. In general, the algorithm can be applied to all kinds of load balancing problems. It is especially well suited to problems if not only idle times should be avoided, but all processors should work on the same level which is deened by a problem dependent weight function. It is also very robust to strongly varying load situations and escapes automatically from trashing situations by …