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W e present a n e w load balancing strategy and its application t o distribuled branch 64 bound algorilhms and demonstrate its efficiency by solving some NPcomplete problems o n a network of u p t o 256 Transputers. T h e parallelizalion of our bran.ch & bound algorithm is fully distributed. Every processor performs the same algorithm but each o n a different part of the solution tree. I n ih,is case it is n,ecessary to distribute subproblems among the processors t o ach.ieve a well balanced workload. O u r load balancing method overcomes the problem of search overhead and idle limes by a n appropriate load model and avoids trashing effects by a feedback control method. Using this strategy we were able t o achieve a speedup of u p to 237.32 o n a 256 processor n.etwork for very short parallel computation times, com.pared t o an, efficien.t sequential alg orit h m .

With nearest-neighbor load-balancing algorithms, a processor makes balancing decisions based on localized workload information and manages workload migrations within its neighborhood. The paper compares a couple of fairly well-known nearest-neighbor algorithms, the dimension-exchange @E) and the difision (DF) methods and their several variants-the average dimension-exchange (ADE), optimally tuned dimension-exchange (ODE), local average diffusion (ADF) and optimally tuned diffusion (ODF). The measures of interest are their efficiency in driving any initial workload distribution to a uniform distribution and their ability in controlling the growth of the variance among the processors' workloads. The comparison is made with respect to both one-port and all-port communication architectures and in consideration of various implementation strategies including synchronouslasynchronous invocation policies and static/dynamic random workload behaviors. It turns out that the dimension-exchange method outperforms the diffusion method in the one-port communication model. In particular, the ODE algorithm is best suited for statically synchronousimplementations of a load-balancing process regardless of its underlying communication models. The strength of the diffusion method is in asynchronous implementations in the all-port communication model; the ODF algorithm performs best in that case. The underlying communication networks considered assume the most popular topologies, the mesh and the torus and their special cases: the hypercube and the k-ary n-cube.Revised 30 M q 199.5 708 C XU E T A L manner and manage workload migrations within the immediate neighborhood[ 1-51, Since they would only spread local workload to nearest neighbors, these algorithms can be easily scaled to operate in massively parallel computers of any size, and would tend to preserve the communication locality inherent in the underlying computations. In general, these algorithms are executed iteratively, with the expectation that successive invocations of local load-balancing would eventually bring about a global balanced state; hence, they give the flexibility of controlling the balance quality over a spectrum of possibilities, from load-sharing (no idle processors coexist with busy processors) to the global balanced state.Nearest-neighbor load-balancing algorithms rely on successive approximations to a global uniform distribution, and hence at each operation, need only be concerned with the direction of workload migration and the issue of how to apportion excess workloads. Among existing load-balancing methods that are characterized by different choic,es of the direction of workload migration [6] we are interested in the diffusion and the dirnensioriexchange methods. These two methods have received a fair amount of attention in recent years. With the diffusion method, a heavily or lightly loaded processor balances its workload with all of its nearest neighbors simultaneously in a load-balancing operation [7,8].With the the dimension-exchange method, a proc...

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