An interesting analogy that Kayvon drew in class when discussing this new blocked assignment strategy was that really what we're doing is trying to maximize the area-to-perimeter ratio of each of our blocked regions. The "area" in this case is the number of elements computed by a single processed (number of dots in a block) and the "perimeter" is the number of elements that have to be communicated to other of processors (number of dots on the boundary of each block). It turns out that geometrically the 2D shape that maximizes this ratio is a square, which is where we get the inspiration for this blocked assignment strategy!
An interesting analogy that Kayvon drew in class when discussing this new blocked assignment strategy was that really what we're doing is trying to maximize the area-to-perimeter ratio of each of our blocked regions. The "area" in this case is the number of elements computed by a single processed (number of dots in a block) and the "perimeter" is the number of elements that have to be communicated to other of processors (number of dots on the boundary of each block). It turns out that geometrically the 2D shape that maximizes this ratio is a square, which is where we get the inspiration for this blocked assignment strategy!