Javascript: Pathfinding in a grid (50000 * 50000) 2d?

Question

Problem

So, let's say one is a 2-dimensional array of integer values ​​representing a map with a grid, for example: +-----+------+-----+-----+-----+ | 10 | 2 | 2 | 4 | 656 | +-----+------+-----+-----+-----+ | 234 | 165 | 724 | 759 | 230 | +-----+------+-----+-----+-----+ | 843 | 734 | 999 | 143 | 213 | +-----+------+-----+-----+-----+ | 242 | 2135 | 131 | 24 | 374 | +-----+------+-----+-----+-----+ | 159 | 464 | 155 | 124 | 151 | +-----+------+-----+-----+-----+ +-----+------+-----+-----+-----+ | 10 | 2 | 2 | 4 | 656 | +-----+------+-----+-----+-----+ | 234 | 165 | 724 | 759 | 230 | +-----+------+-----+-----+-----+ | 843 | 734 | 999 | 143 | 213 | +-----+------+-----+-----+-----+ | 242 | 2135 | 131 | 24 | 374 | +-----+------+-----+-----+-----+ | 159 | 464 | 155 | 124 | 151 | +-----+------+-----+-----+-----+

2d indices represent the coordinates of a cell on the map, and the values ​​in the array represent the relative difficulty of crossing the terrain of this cell - for example, 999 can be thick blackberries, while 2,3,4 can be a slightly inclined path ... or something like that.

Now we want to find the easiest way from [x, y] on the grid to [q, r] on the grid (where the sum of the steps is the smallest possible, in other words)

Problem area

This needs to be launched in a modern browser, where a rather spartan map is displayed, and we will draw a line from [x, y] to [q, r] through all the alternating vertices after the user entered [Q, R]. Conveniently, [X, Y] is always the same (say [0,0] for simplicity)

So use the Jikstra algorithm or *!

So, my first instinct was modeling the array in the form of a graph, applying the Dijkstra algorithm and working from there. And in the case above, with a 5x5 grid, this works fine. I move each index of the array and use the value and adjacent values ​​to generate a node with weighted edges for all its neighbors. This creates a graph in which I can apply the Jikstra algorithm to.

However, in practice, I will work with arrays up to 50,000 x 50,000 in size! This is 250 million!

Obviously, creating an on-the-fly graph to run the Dijkstrass algorithm is not applicable. My next idea was to pre-compute the paths (the dataset has been fixed), save them on the server and call back when we get the destination [q, r] ... but this is 250,000,000 paths ... even if I ran it in less than a second (which I don’t think it would be), it will take several years to calculate all the paths ...

I think I might need a different approach, but I'm not sure how I can do this?

Answer 1

Do not create an explicit graph (road signs) - use coordinate pairs to represent nodes in the queue and change the Dijkstra implementation to work directly with your 2d array representation.

Use an array similar to the cost array to store (initially estimated) distances calculated by the algorithm.

Dijkstra will calculate the costs for all nodes in one pass, so if your starting point is fixed, starting it once should be sufficient - there is no need to run it millions of times.

PS: Created Jsfiddle, on which Dijkstra runs on images: https://goo.gl/5GWwMF

Calculates distances to all points with the mouse, where darker pixels are interpreted as more expensive ...

It becomes slower with large images, but still has not been able to break it, but I think that your data will run out of memory in your browser.

The Dijkstra implementation uses the following interface to access the graph — I think it should be straight ahead to provide on top of your data structure without explicitly creating a “traditional” graph data structure with explicit nodes and edges in memory:

 /** * The interface the Dijkstra implementation below uses * to access the graph and to store the calculated final * and intermediate distance data. * * @Interface */ Graph = function() {}; /** * Returns the current distance for the given node. * @param {Object} node * @return {number} */ Graph.currentDistance = function(node) {}; /** * Stores the current distance for the given node. * @param {Object} node * @param {number} distance */ Graph.setCurrentDistance = function(node, distance) {}; /** * Returns an array of connected nodes for the given node, * including the distances. * * @param {Object} * @return {Array<{cost:number, node:Object}>} */ Graph.connections = function(node) {}; 

PPS: Added code to display shortes path for all clicks after the first click. Also fixed a bug allowing diagonal movement: https://goo.gl/wXGwiv

So in conclusion, although this probably does not scale to 50k x 50x in the browser, I think it shows that Dijkstra running on arrays is worth a try on the server side and that an array of identical size data array is all what is needed to store all the shortest paths from one point.