Parallel branch and bound on fine-grained hypercube multiprocessors

In this paper, we study parallel branch and bound on fine grained hypercube multiprocessors. Each processor in a fine grained system has only a very small amount of memory available. Therefore, current parallel branch and bound methods for coarse grained systems (≤ 1000 nodes) cannot be applied, since all these methods assume that every processor stores the path from the node it is currently processing back to the node where the process was created (the back-up path). Furthermore, the much larger number of processors available in a fine grained system makes it imperative that global information (e.g. the current best solution) is continuously available at every processor; otherwise the amount of unnecessary search would become intolerable. We describe an efficient branch-and-bound algorithm for fine grained hypercube multiprocessors. Our method uses a global 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 current nodes may decide whether they need to create new children, be pruned, or remain unchanged. We describe an algorithm that, based on these decisions, updates the current back-up paths and distributes global information in O(log m) steps, where m is the current number of nodes. This method also includes dynamic allocation of search processes to processors and provides optimal load balancing. Even if very drastic changes in the set of current nodes occur, our load balancing mechanism does not suffer any slow down

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