Parallel branch and bound on fine-grained hypercube multiprocessors

An efficient branch and bound algorithm for fine-grained hypercube multiprocessors is presented. The method uses a global storage allocation scheme where all processors collectively store all back-up paths such that each processor needs to store only a constant amount of information. At each iteration of the algorithm, all nodes of the current back-up tree may decide whether they need to create new children, be pruned, or remain unchanged. An algorithm that, on the basis of these decisions, updates the current back-up tree and distributes global information in O(log m) steps, where m is the current number of nodes, is described. This method also provides a dynamic allocation mechanism that obtains optimal load balancing. Another important property of the method is that, even if very drastic changes in the current back-up tree occur, the performance of the load balancing mechanism remains constant. The method is currently being implemented on the Connection Machine