The balancing of the partition of the Gröbner basis seems to be a necessary condition for an efficient parallel implementation, although it does not affect the correctness of the algorithm. Because the result of each new polynomial's reduction is unknown in advance, any global iteration may create some imbalance. Yet it is not clear whether the cost of re-balancing is always smaller than the speedup it provides in subsequent iterations.
Faced with this dilemma we have designed two versions of the algorithm: with and without dynamic balancing, so that performance tests may help to compare them. Moreover, the algorithm with balancing is driven by a threshold value so as to explore even further the tradeoff between more/less re-balancing.