<P> This algorithm is a trivial modification from the serial version, and its speedup is not impressive: when executed on an infinite number of processors, it runs in Θ (n) time, which is only a Θ (log n) improvement on the serial version . A better result can be obtained by using a parallelized merge algorithm, which gives parallelism Θ (n / (log n)), meaning that this type of parallel merge sort runs in </P> <Dl> <Dd> Θ ((n log ⁡ n) ⋅ (log ⁡ n) 2 n) = Θ ((log ⁡ n) 3) (\ displaystyle \ Theta \ left ((n \ log n) \ cdot (\ frac ((\ log n) ^ (2)) (n)) \ right) = \ Theta ((\ log n) ^ (3))) </Dd> </Dl> <Dd> Θ ((n log ⁡ n) ⋅ (log ⁡ n) 2 n) = Θ ((log ⁡ n) 3) (\ displaystyle \ Theta \ left ((n \ log n) \ cdot (\ frac ((\ log n) ^ (2)) (n)) \ right) = \ Theta ((\ log n) ^ (3))) </Dd> <P> time if enough processors are available . Such a sort can perform well in practice when combined with a fast stable sequential sort, such as insertion sort, and a fast sequential merge as a base case for merging small arrays . </P>

When does the worst case of merge sort occur