Fig. 4.

Conceptual idea of bit-vector merging. Red bars represent bit-vectors, which are stored in memory. Gray bars represent input/output columns, which are never stored explicitly, but represented implicitly by the respective bit-vectors. The variable D is split into chunks of size $O(\text{log}\hspace{0.17em}m)$, where the bits in each chunk encode the difference between a particular row in S^A and S^B, as indicated by green lines. The values in each chunk are used to compute the respective bits in $M_{A>B}$ and $M_{B>A}$. In each iteration, the chunks are updated to represent a difference of S^A and S^B one row further down, indicated by down arrows. Once $M_{A>B}$ and $M_{B>A}$ have been computed, the ‘picking mask’ M_p is computed in parallel (horizonal arrows) and used in the final merging step (blue box)