Finding defectives on a line by random docking and interval group tests

Journal article, 2017

Suppose that some of the n elements of a totally ordered structure is defective, and several repair robots are at our disposal. They can dock at a random element, move at unit speed or leave, and send each other signals if there is no defective between them. We show that, by using only two robots that obey simple rules, the defective can be localized in square-root(n) time, which is also optimal. A variation of our strategy needs three robots but has a more predictable behaviour. The model is motivated by a conjectured DNA repair mechanism, and it combines group testing with geometric search.