Three structures on the input chosen against them, n = 2,048

Three structures on the input chosen against them, n = 2,048

Each pair is one problem, solved deterministically and randomly, measured on the input that is worst for the deterministic version. The bars are logarithmic because the pairs are: 83×, 79×, 205×. The deterministic guarantees are all average-case ones — true of most inputs, and about the data. The randomised guarantees are expected-case, true of every input, and about the algorithm's own coins. Only the second kind survives somebody choosing the input.

Drawn at 700 × 318, wide on the page. Everything above is what guarantee-under-attack returns with no arguments; the caption is the generator's own, computed from the numbers in the drawing rather than written beside it.

2 essays call guarantee-under-attack. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about — which is what optcheck and figfill exist to catch.