Sun, 23 Oct 2022
Yesterday I described an algorithm that locates the ‘bad’ items among a set of items, and asked:
The answer is: this is group testing, or, more exactly, the “binary splitting” version of adaptive group testing, in which we are allowed to adjust the testing strategy as we go along. There is also non-adaptive group testing in which we come up with a plan ahead of time for which tests we will perform.
I felt kinda dumb when this was pointed out, because:
Oh well. Thanks to everyone who wrote in to help me! Let's see, that's Drew Samnick, Shreevatsa R., Matt Post, Matt Heilige, Eric Harley, Renan Gross, and David Eppstein. (Apologies if I left out your name, it was entirely unintentional.)
I also asked:
Wikipedia is quite confident about this:
Eric Harley said:
Yeah, now I wonder too. Surely there must be some coin-weighing puzzles in Sam Loyd or H.E. Dudeney that predate Dorfman?
Dorfman's original algorithm is not the one I described. He divides the items into fixed-size groups of n each, and if a group of n contains a bad item, he tests the n items individually. My proposal was to always split the group in half. Dorfman's two-pass approach is much more practical than mine for disease testing, where the test material is a body fluid sample that may involve a blood draw or sticking a swab in someone's nose, where the amount of material may be limited, and where each test offers a chance to contaminate the sample.
Wikipedia has an article about a more sophisticated of the binary-splitting algorithm I described. The theory is really interesting, and there are many ingenious methods.
Thanks to everyone who wrote in. Also to everyone who did not. You're all winners.
[ Addendum 20221108: January First-of-May has brought to my attention section 5c of David Singmaster's Sources in Recreational Mathematics, which has notes on the known history of coin-weighing puzzles. To my surprise, there is nothing there from Dudeney or Loyd; the earliest references are from the American Mathematical Monthly in 1945. I am sure that many people would be interested in further news about this. ]