Pipe Sort

Search Lattice For CUBE : is a graph where a vertex represents a group-by of the CUBE. A directed edge connects group-by i to group-by j, whenever j can be generated from i and j has exactly one attribute less than i.

A(e_ij) is the cost of computing j from i when i is already sorted.

S(e_ij) is the cost of computing j from i when i is not sorted.