14 Facts About Group testing

In statistics and combinatorial mathematics, group testing is any procedure that breaks up the task of identifying certain objects into tests on groups of items, rather than on individual ones.

Familiar example of group testing involves a string of light bulbs connected in series, where exactly one of the bulbs is known to be broken.

Group testing has many applications, including statistics, biology, computer science, medicine, engineering and cyber security.

Unlike many areas of mathematics, the origins of group testing can be traced back to a single report written by a single person: Robert Dorfman.

Group testing can be extended by considering scenarios in which there are more than two possible outcomes of a test.

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Group testing with inhibitors is a variant with applications in molecular biology.

Concept of group testing was first introduced by Robert Dorfman in 1943 in a short report published in the Notes section of Annals of Mathematical Statistics.

Dorfman's report – as with all the early work on group testing – focused on the probabilistic problem, and aimed to use the novel idea of group testing to reduce the expected number of tests needed to weed out all syphilitic men in a given pool of soldiers.

Group testing was first studied in the combinatorial context by Li in 1962, with the introduction of Li's -stage algorithm.

In general, finding optimal algorithms for adaptive combinatorial group testing is difficult, and although the computational complexity of group testing has not been determined, it is suspected to be hard in some complexity class.

One of the key insights in non-adaptive group testing is that significant gains can be made by eliminating the requirement that the group-testing procedure be certain to succeed, but rather permit it to have some low but non-zero probability of mis-labelling each item .

Therefore, the goal of group testing is to come up with a method for choosing a 'short' series of tests that allow to be determined, either exactly or with a high degree of certainty.

Useful property of -disjunct Group testing matrices is that, with up to defectives, every non-defective item will appear in at least one test whose outcome is negative.

Generality of the theory of group testing lends it to many diverse applications, including clone screening, locating electrical shorts; high speed computer networks; medical examination, quantity searching, statistics; machine learning, DNA sequencing; cryptography; and data forensics.