Complex sentence: There is only one published estimate (the one below) on the complexity of the sieve of Atkin, and the estimates for the sieve of Eratosthenes must use the same optimizations, otherwise the comparison is totally meaningless.
Split into simpler sentences: There is only one published estimate (the one below) on the complexity of the sieve of Atkin, which we are therefore bound to use. The estimates for the sieve of Eratosthenes then must use the same optimizations, otherwise the comparison is totally meaningless.