Why it matters

Pairwise independence saves randomness. Understanding shapes randomization theory.

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The architecture

Family H such that for pair (x, y), (h(x), h(y)) uniform + independent.

Small seed suffices.

Pairwise indep hashFamily Hsmall sizePair independence(h(x), h(y)) uniform + indepApplicationshashing + derandUniversal hashing + streaming algorithms use; small seed suffices for many bounds
Pairwise indep.
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How it works end to end

Linear hash functions h(x) = ax + b mod p.

Small family suffices.

Applications: streaming, load balancing.