let path = require('ngraph.path');
let pathFinder = path.aStar(graph);

// now we can find a path between two nodes:
let fromNodeId = 40;
let toNodeId = 42;
let foundPath = pathFinder.find(fromNodeId, toNodeId);
// foundPath is array of nodes in the graph

Example above works for any graph, and it's equivalent to unweighted Dijkstra's algorithm.

Weighted graph

Let's say we have the following graph:

let createGraph = require('ngraph.graph');
let graph = createGraph();

graph.addLink('a', 'b', {weight: 10});
graph.addLink('a', 'c', {weight: 10});
graph.addLink('c', 'd', {weight: 5});
graph.addLink('b', 'd', {weight: 10});

We want to find a path with the smallest possible weight:

let pathFinder = aStar(graph, {
  // We tell our pathfinder what should it use as a distance function:
  distance(fromNode, toNode, link) {
    // We don't really care about from/to nodes in this case,
    // as link.data has all needed information:
    return link.data.weight;
  }
});
let path = pathFinder.find('a', 'd');

This code will correctly print a path: d <- c <- a.

Guided (A-Star)

When pathfinder searches for a path between two nodes it considers all neighbors of a given node without any preference. In some cases we may want to guide the pathfinder and tell it our preferred exploration direction.

For example, when each node in a graph has coordinates, we can assume that nodes that are closer towards the path-finder's target should be explored before other nodes.

let createGraph = require('ngraph.graph');
let graph = createGraph();

// Our graph has cities:
graph.addNode('NYC', {x: 0, y: 0});
graph.addNode('Boston', {x: 1, y: 1});
graph.addNode('Philadelphia', {x: -1, y: -1});
graph.addNode('Washington', {x: -2, y: -2});

// and railroads:
graph.addLink('NYC', 'Boston');
graph.addLink('NYC', 'Philadelphia');
graph.addLink('Philadelphia', 'Washington');

When we build the shortest path from NYC to Washington, we want to tell the pathfinder that it should prefer Philadelphia over Boston.

let pathFinder = aStar(graph, {
  distance(fromNode, toNode) {
    // In this case we have coordinates. Lets use them as
    // distance between two nodes:
    let dx = fromNode.data.x - toNode.data.x;
    let dy = fromNode.data.y - toNode.data.y;

    return Math.sqrt(dx * dx + dy * dy);
  },
  heuristic(fromNode, toNode) {
    // this is where we "guess" distance between two nodes.
    // In this particular case our guess is the same as our distance
    // function:
    let dx = fromNode.data.x - toNode.data.x;
    let dy = fromNode.data.y - toNode.data.y;

    return Math.sqrt(dx * dx + dy * dy);
  }
});
let path = pathFinder.find('NYC', 'Washington');

With this simple heuristic our algorithm becomes smarter and faster.

It is very important that our heuristic function does not overestimate actual distance between two nodes. If it does so, then algorithm cannot guarantee the shortest path.

Performance

Internally, I'm using heap-based priority queue, built specifically for path finding. I modified it, so that changing priority of any element in the queue takes O(lg n) time.

I measured performance of this implementation on New York City roads graph (733,844 edges, 264,346 nodes). It was done by solving 250 random path finding problems. Each algorithm was solving the same set of problems. Table below shows required time to solve one problem.

	Average	Median	Min	Max	p90	p99
A* greedy (suboptimal)	32ms	24ms	0ms	179ms	73ms	136ms
NBA*	44ms	34ms	0ms	222ms	107ms	172ms
A*, unidirectional	55ms	38ms	0ms	356ms	123ms	287ms
Dijkstra	264ms	258ms	0ms	782ms	483ms	631ms

"A* greedy" converged the fastest, however, as name implies the found path is not necessary globally optimal. The algorithm performs two searches from both ends and quits as soon as both searches meet.

Which method to choose?

With many options available, it may be confusing whether to pick Dijkstra or A*.

I would pick Dijkstra if there is no way to guess a distance between two arbitrary nodes in a graph. If we can guess distance between two nodes - pick A*.

Among algorithms presented above, I'd recommend A* greedy if you care more about speed and less about accuracy. However if accuracy is your top priority - choose NBA*. This is a bi-directional, optimal A* algorithm with very good exit criteria. You can read about it here: https://repub.eur.nl/pub/16100/ei2009-10.pdf

license

MIT