Brick Sort

is a sorting algorithm that sorts by making brick passes with a gap sequence, like a Comb Sort but with brick passes. A brick pass consists of starting i at 0, then compare-exchanging i and i+gap and incrementing i, while i<gap, the first part is taking i from 0 to gap-1, from 2*gap to 3*gap-1, from 4*gap to 5*gap-1, etc. the second part is taking the i from gap to 2*gap-1, from 3*gap to 4*gap-1, etc. so both parts are parallelisable and the pass is complete.

Shrink factor
implemented with a shrink factor. The gap is divided by a constant shrink factor with truncation, and when the gap reaches 1, it continues the 1 passes until not swapped (Odd-Even Sort). This has the best case of O (n×log n), whereas the average and worst case are conjectured to be O (n²). "Empirical Result (Lemke, Sedgewick, 1994) Replacing the h-sort in Shellsort by an h-brick pass gives an algorithm that nearly always sorts when the increment sequence is geometric, with ratio less than 1.22."

3-smooth gaps
A gap sequence requiring only one 1 pass, is use 3-smooth numbers. Each gap is preceded by two and three times larger gaps. So, 1 is preceded by 2 and 3, but 2 in turn is preceded by 4 and 6, and 3 is preceded by 6 and 9, and so on. It may be implemented by recursively sorting with gap 3 then use powers of 2, or recursively sorting with gap 2 then use powers of 3. It has O (n×(log n)²) best case, average case, and worst case and it is a sorting network. This works as a Comb Sort sequence but it works for as well.