Can't see your picture...
You want to look at the A* algorithm for tile based (or node based) pathfinding http://en.wikipedia.org/wiki/A*_search_algorithm
which is usually more efficient than Djikstra's algorithm which is basically just a flood fill.
EDIT: I can see your picture now, can't see any tiles though ;)
think that all rectangles are tiles (could be more then one in same place) and all other is alot of white rectangles that was just fast drawing
But maybe not tiled based game would be better? Talking about pathfinding