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A technique to improve performance on distributed memory machines of irregularly structured Grobner basis computations is developed. In parallel Grobner basis computation, at every step many tasks are executed in parallel by relating the dependencies present in sequential computation. In this relaxation approach, the idle time spent by processors at k/sup th/ step can be reduced by synchronizing p processors when r out of NT/sub k/(r/spl les/NT/sub k//spl les/p) tasks (instead of NT/sub k/) are complete. The analysis presented in this paper shows that, in theory, the improvement in speedup can be as much as lnp when the task distribution is close to exponential. In 70-75% of the experiments carried on IBM SP2 and Intel Paragon, this quasi-barrier technique improved speedup.