JPS+: Over 100x Faster than A* (2015) [video]

D* can be pathologically slower than repeated A* searches under such conditions.

They may not solve all your problems or even any of them (hard to tell knowing nothing about your game, after all), but I was absolutely dumbfounded when I played around with them at how cheaply you can get some rather complex (seeming) behaviors (e.g. put the player and some enemies in a maze, give the players a scent that strongly attracts the enemies, but also give them a slight scent that makes them repulse each other, and they'll automagically split up and surround the player).

At the very least, if you're stuck with what you're doing at the moment, play around with those, and maybe you can at least find a use for them that frees up some processing resources for precise path finding where nothing short of it will do.

All shortest paths are either a straight line, or consist of the straight line from the original location to an outside corner, a series of straight lines between outside corners, and a straight line from an outside corner to the destination. (An outside corner is any 2x2 square with three walkable and one wall tile.)

You can easily find all the outside corners. You can find which pairs of outside corners can be walked between using N^2 ray casts. Once you've done that, you can detect when an outside corner has been removed and drop it from the map, or detect when one has been created and perform N ray casts to add it to your pathing list.

Running A* on the resulting structure is really fast, because it's smaller and more connected than a tile list. The slowest remaining part is finding the corners immediately reachable from your start/end points, which I think could also be sped up but I'd benchmark it before worrying about that.

I would say that you have the causation reversed: we just don't bother doing large matrix multiplications, because they're so expensive (and yet still don't usually cross the intercepts into making the "better" algorithms worth it, due to those algorithms having ridiculous constant coefficients.)

I would love to run Floyd-Warshall on my 40-million point network graph—but it just ain't gonna happen.

Global routing is a high-level routing approach: routing millions of nets (= connections usually between 1 output pin of a gate and N input pins of other gates) on a grid graph with potentially billions of nodes is an extremely difficult Steiner tree problem.

To get good solutions, a common approach is to first solve the problem on a much coarser graph where edges have capacities. I.e. instead of having to place all connections disjointly, edges in the graph can accommodate a number of parallel connections.

A later detailed routing step will produce the actual disjoint routes while following the outline that was obtained during global routing.

There are certainly things you shouldn't delegate to an autorouter, but in the same way, the trend towards hair-shirt-wearing insistence that everything be done manually is a productivity cost.

It's no different to programmers who insist on hand-optimizing assembler: Rarely necessarily any more and usually done more out of ego.

The really competent engineers use the tools for the bulk of the problem, and fix up by hand where it makes sense.