Algorithm Optimization - Shortest Route Between Multiple Points

Question

Problem: I have a large collection of points. Each of these points has a list with references to other points with the distance between them already calculated and stored. I

Answer 1

It appears that the edges of your graph are bidirectional. In this case, the algorithm you're looking for is Dijkstra's algorithm.

Answer 2

In generally you should to strict bad variants... I think you should use some variations of Branch_and_bound method http://en.wikipedia.org/wiki/Branch_and_bound

Answer 3

This sounds Travelling Salesman-esque? One solution is to use an optimisation technique such as an evolutionary algorithm. Currently you are doing an exhaustive search, which will get very slow very quickly. But I think this is pretty much a travelling salesman problem and it has been tackled for several decades if not centuries, and such there are several possible ways of attack. Google is your friend.

Answer 4

This is the very common and real time situation any one can fall in.Google map user interface gives you the path in the same order, you add in the destination list. it doesn't give you the optimal path though their own Google maps API provide the solution.

Google maps API provides the solution for this. In the request to find out the path you have to provide the flag 'optimizeWaypoints: true,'. The request will seem like this.

var request = {
            origin: start,
            destination: end,
            waypoints: waypts,
            optimizeWaypoints: true,
            travelMode: google.maps.TravelMode.DRIVING
        };

and you can see whole code of the utility in the view source as complete utility is developed in javascript and HTML.

I hope it will help.

Answer 5

Answering to the updated post, your solution of checking every possibility is optimal (at least, noone has discovered better algorithms so far). Yes, that's a travelling salesman, whose essense is not touching every city, but touching every city once. If you don't want to search for best solution possible, you may find it useful to use heuristics that work faster, but allow for limited discrepancy from ideal solution.

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For future answerers: Floyd-Warshall algorithm and all Floyd-like variations are inapplicable here.

Answer 6

Either bredth first search as norheim.se said or Dijkstra's algorithm would be my suggestion as well.