Unstructured Tree Search on SIMD Parallel Computers

In this paper, we present new methods for load balancing of unstructured tree computations on large-scale SIMD machines, and analyze the scalability of these and other existing schemes. An e cient formulation of tree search on a SIMD machine comprises of two major components: (i) a triggering mechanism, which determines when the search space redistribution must occur to balance search space over processors; and (ii) a scheme to redistribute the search space. We have devised a new redistribution mechanism and a new triggering mechanism. Either of these can be used in conjunction with triggering and redistribution mechanisms developed by other researchers. We analyze the scalability of these mechanisms, and verify the results experimentally. The analysis and experiments show that our new load balancing methods are highly scalable on SIMD architectures. Their scalability is shown to be no worse than that of the best load balancing schemes on MIMD architectures. We verify our theoretical results by implementing the 15-puzzle problem on a CM-21 SIMD parallel computer. This work was supported by Army Research O ce grant #28408-MA-SDI to the University of Minnesota and by the Army High Performance Computing Research Center at the University of Minnesota. CM-2 is a registered trademark of Thinking Machines Corporation.