Comparisons against peak auxiliary space, n = 8,192

Comparisons against peak auxiliary space, n = 8,192

One point per sort, both axes logarithmic, cheapest and smallest towards the bottom left. The line joins the Pareto frontier — the 5 algorithms that nothing else beats on both counts at once. The 5 points off it are dominated, and being dominated is a stronger statement than being slower: there is no weighting of these two costs under which they are the right choice. This is the honest answer to "which sorting algorithm", and it is a shape rather than a name.

Drawn at 700 × 430, wide on the page. Everything above is what time-space-frontier returns with no arguments; the caption is the generator's own, computed from the numbers in the drawing rather than written beside it.

4 essays call time-space-frontier. 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.