I was reading the paper on Jump consistent hashing, and I'm having some trouble understanding one particular line (page 5, paragraph 2)
"Since we want P(j ≥ i) = (b+1) / i, we set P(j ≥ i) iff r ≤ (b+1) / i."
My understanding is that:
- P(j ≥ i) is the probability that a key "jumps"/moves to a different bucket after bucket#i
- r is a pseudo random number between [0, 1) with a uniform distribution
- b is the last bucket# for which a jump occurred for this key
In particular, I am having trouble understanding this phrase: "we set P(j ≥ i) iff".
Set it to what? Do they mean to say "We want a key to jump to a different bucket ≥ i with a random probability r. This means that P(j ≥ i) ≥ r, which implies that (b+1)/i ≥ r. Hence the smallest such bucket number is obtained by the equation i = floor((b+1)/r)"?