Balanced allocations and double hashing

With double hashing, for an item x, one generates two hash values f(x) and g(x), and then uses combinations (f(x) +ig(x)) mod n for i=0,1,2,... to generate multiple hash values from the initial two. We show that the performance difference between double hashing and fully random hashing appears negligible in the standard balanced allocation paradigm, where each item is placed in the least loaded of d choices, as well as several related variants. We perform an empirical study, and consider multiple theoretical approaches. While several techniques can be used to show asymptotic results for the maximum load, we demonstrate how fluid limit methods explain why the behavior of double hashing and fully random hashing are essentially indistinguishable in this context.