Scalability of Massively Parallel Depth-first Search

We analyze and compare the scalability of two generic schemes for heuristic depthrst search on highly parallel MIMD systems. The rst one employs a task attraction mechanism where the work packets are generated on demand by splitting the donor's stack. Analytical and empirical analyses show that this stack-splitting scheme works e ciently on parallel systems with a small communication diameter and a moderate number of processing elements. The second scheme, search-frontier splitting, also employs a task attraction mechanism, but uses pre-computed work packets taken from a search-frontier level of the tree. At the beginning, a search-frontier is generated and stored in the local memories. Then, the processors expand the subtrees of their frontier nodes, communicating only when they run out of work or a solution has been found. Empirical results obtained on a 32 32 = 1024 node MIMD system indicate that the search-frontier splitting scheme incurs fewer overheadsand scales better than stack-splitting on large message-passing systems. Best results were obtained with an iterative-deepening variant that improves the work-load balance from one iteration to the next.