Editing Open Problems:58
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{{Header | {{Header | ||
+ | |title=Signatures for set equality | ||
|source=dortmund12 | |source=dortmund12 | ||
|who=Rasmus Pagh | |who=Rasmus Pagh | ||
}} | }} | ||
− | Given $S\subseteq\{1,..n\}$, we would like to construct a fingerprint so that later, given fingerprints of two sets, we can check the equality of the two sets | + | Given $S\subseteq\{1,..n\}$, we would like to construct a fingerprint so that later, given fingerprints of two sets, we can check the equality of the two sets. |
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− | '''Question | + | There are (at least) two possible solutions to the problem: |
+ | * $h(S)=\sum_{i\in S} x^i\mod p$ for random $x\in \Z_p$. Update time would be roughly $\log p=\Omega(\log n)$. One would like to obtain a better update time. | ||
+ | * $h(S)=\prod_{i\in S} (x-i) \mod p$, and random $x$. Insertion can be done in constant time. But the fingerprint is not linear. | ||
+ | |||
+ | '''Question''': Can we construct a fingerprint that achieves constant update time and is linear, while using $O(\log n)$ random bits? Ideally updates would include insertions and deletions. |