Suppose you're given a 2D grid with 0/1s corresponding to impassable/passable locations and a given pair of source and target locations in the grid. Each location not on the boundary has 4 neighbors ...

Our model shows that by considering the product graph in terms of its factors, the 2D companion shift is a 2D directed grid with b.c. in both directions. We show that, under this 2D companion model, ...