Faster pathfinding using Jump Point Search(harablog.wordpress.com)
harablog.wordpress.com
Faster pathfinding using Jump Point Search
http://harablog.wordpress.com/2011/09/07/jump-point-search/
16 comments
Any game vaguely resembling Wolfenstein uses a uniform-cost grid.
What a strange use of the word "symmetric": "Two grid paths are symmetric if they share the same start and end point and one can be derived from the other by swapping the order of the constituent vectors."
How so? That would be a 2-fold rotational symmetry, wouldn't it?
http://en.wikipedia.org/wiki/Rotational_symmetry
http://en.wikipedia.org/wiki/Rotational_symmetry
Two pieces are rotated, that doesn't make the whole thing symmetric.
I can see how defining symmetry for a pathfinding domain might be non-intuitive. What the quoted definition is trying to communicate is that paths sharing such a relation are permutations of one another and thus, symmetric.
I understand that they are "equivalent" in a certain sense, but "symmetric"?
Two equivalent paths share the same endpoints and have the same length. Two symmetric paths also have these properties but they can also be shown to be permutations of each other.
Seeing the permutation property isn't straightforward until you change your definition of a path: from an ordered sequence of edges to an ordered sequence of vectors.
Take the following two paths as examples:
p1 = {up, up, up, right, right, right} p2 = {up, right, up, right, up, right}
Not only are they equivalent but I can derive one from the other by just changing the order of the moves.
Such symmetries are plentiful on grid maps: as soon as you have a large open area, you introduce lots of possible ways to cross it.
Seeing the permutation property isn't straightforward until you change your definition of a path: from an ordered sequence of edges to an ordered sequence of vectors.
Take the following two paths as examples:
p1 = {up, up, up, right, right, right} p2 = {up, right, up, right, up, right}
Not only are they equivalent but I can derive one from the other by just changing the order of the moves.
Such symmetries are plentiful on grid maps: as soon as you have a large open area, you introduce lots of possible ways to cross it.
Is it just me or does the Vanilla-A* algorithms look too bad? I mean especailly in the second image [(d) A* (Adaptive Depth)], why does it search behind itself?
This behaviour exists because A*'s heuristic function assumes there are no obstacles when estimating the remaining distance to reach the goal. As the difference between the heuristic estimate to the goal and the actual distance increases, some nodes "behind" the start location will appear more promising than other nodes which are eventually proven to be on the optimal path.
Because that's how A star works :)
It's a graph search. Imagine adding an out-of-plane edge that travels from behind the starting point to the goal. Since taming that path could be optimal it has to check - it doesn't attempt to reason that such a path would necessarily be obstructed by what's been explored thus far. It's just a graph search.
It's a graph search. Imagine adding an out-of-plane edge that travels from behind the starting point to the goal. Since taming that path could be optimal it has to check - it doesn't attempt to reason that such a path would necessarily be obstructed by what's been explored thus far. It's just a graph search.
Suppose there was a wall or other obstacle between you and the destination. Then you might have to go "back" to find a way around. Vanilla A* can't "know" whether this is the case, so it searches outwards in all directions, using the heuristic to weight the search towards paths that are getting us closer to the destination.
Any speed ranking against alternatives?
In the paper we make an apples-to-apples comparison with a recent optimality-preserving state-space reduction method called Swamps and an apples-to-oranges comparison with an approximate pathfinding algorithm, HPA*.
Swamps is a nice technique for narrowing the scope of the current search; it achieves ~5x maximum speedup and could be combined with Jump Point Search to go faster still.
The comparison to HPA is summarised in the article. Additional evaluations are the subject of further work :)
Swamps is a nice technique for narrowing the scope of the current search; it achieves ~5x maximum speedup and could be combined with Jump Point Search to go faster still.
The comparison to HPA is summarised in the article. Additional evaluations are the subject of further work :)
How useful are uniform-cost grids? Every implementation of A* I've ever used has been applied to varying-cost grids.