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We propose and evaluate a parallel "decomposite best-first" search branch-and-boundalgorithm (dbs) for MIN-based multiprocessor systems. We start with a new probabilisticmodel to estimate the number of evaluated nodes for a serial best-first searchbranch-and-bound algorithm. This analysis is used in predicting the parallel algorithmspeed-up. The proposed algorithm initially decomposes a problem into N subproblems,where N is the number of processors available in a multiprocessor. Afterwards, eachprocessor executes the serial best-first search to find a local feasible solution. Localsolutions are broadcasted through the network to compute the final solution. Aconflict-free mapping scheme, known as the step-by-step spread, is used for subproblemdistribution on the MIN. A speedup expression for the parallel algorithm is then derivedusing the serial best-first search node evaluation model. Our analysis considers bothcomputation and communication overheads for providing realistic speed-up.Communication modeling is also extended for the parallel global best-first searchtechnique. All the analytical results are validated via simulation. For large systems, whencommunication overhead is taken into consideration, it is observed that the paralleldecomposite best-first search algorithm provides better speed-up compared to otherreported schemes.