グループテスト
↑ The number of tests, t {\displaystyle t} , must scale as t = O ( d 2 log d  n ) {\displaystyle t=O\left(d^{2}\log _{d}n\right)} for deterministic designs, compared to t = O ( d log 2  n ) {\displaystyle t=O(d\log _{2}n)} for designs that allow arbitrarily small probabilities of error (as d → ∞ {\displaystyle d\to \infty } and n → ∞ {\displaystyle n\to \infty } ).
↑ One must be careful to distinguish between when a test reports a false result and when the group-testing procedure fails as a whole. It is both possible to make an error with no incorrect tests and to not make an error with some incorrect tests. Most modern combinatorial algorithms have some non-zero probability of error (even with no erroneous tests), since this significantly decreases the number of tests needed.
Data forensics is a field dedicated to finding methods for compiling digital evidence of a crime. Such crimes typically involve an adversary modifying the data, documents or databases of a victim, with examples including the altering of tax records, a virus hiding its presence, or an identity thief modifying personal data.
A common tool in data forensics is the one-way cryptographic hash. This is a function that takes the data, and through a difficult-to-reverse procedure, produces a unique number called a hash. Hashes, which are often much shorter than the data, allow us to check if the data has been changed without having to wastefully store complete copies of the information: the hash for the current data can be compared with a past hash to determine if any changes have occurred.
Otherwise, use a binary search to identify one defective and an unspecified number, called x {\displaystyle x} , of non-defective items; set n := n − 1 − x {\displaystyle n:=n-1-x} and d := d − 1 {\displaystyle d:=d-1} . Go to step 1.
The generalised binary-splitting algorithm requires no more than T {\displaystyle T} tests where T = { n n ≤ 2 d − 2 ( α + 2 ) d + p − 1 n ≥ 2 d − 1 {\displaystyle T={\begin{cases}n&n\leq 2d-2\\(\alpha +2)d+p-1&n\geq 2d-1\end{cases}}} .