Minimum Tile Ordering

Question

Minimizing Tile Re-ordering Problem:

Suppose I had the following symmetric 9x9 matrix, N^2 interactions between N particles:

(1,2) (2,9) (4,5) (4,6) (5         


        

Answer 1

You can look for a data structure like kd-tree, R-tree, quadtree or a space filling curve. Especially a space filling curve can help because it reduce the dimension and also reorder the tiles and thus can add some new information to the grid. With a 9x9 grid it's probably good to look into peano curves. The z order morton curve is better for power of 2 grids.