Shortest Path

This single source shorteset path can be expressed as follows: given a weighted directed graph, find the minimum path between a vertex u and any other vertex v.

Depending on the properties of the weights and the graph, different algorithms can be applied:

• positive weights, graph is a Directed Acyclic Graph: DagShortestPathAlgorithm,
• positive weights: DijsktraShortestPathAlgorithm,
• positive weights, with heuristics: AStartShortestPathAlgorithm,
• positive or negative weights: BellmanFordShortestPathAlgorithm

Quick example

The AlgorithmExtensions contains extension methods to compute the shortest path without the ugly details.

IVertexAndEdgeListGraph<int, Edge<int>> cities = ...; // a graph of cities
Func<Edge<int>, double> cityDistances = ...; // a delegate that gives the distance between cities

int sourceCity = 0; // starting city
int targetCity = 0; // ending city

// vis can create all the shortest path in the graph
// and returns a delegate that can be used to retreive the graphs
TryGetFunc<int, IEnumerable<int>> tryGetPath = cities.ShortestPathsDijkstra(cityDistances, sourceCity);
// enumerating path to targetCity, if any
IEnumerable<Edge<int>> path;
if (tryGetPath(targetCity, out path))
    foreach (var e in path)
        Console.WriteLine(e);

Full example

This sample shows how to compute the shortest path between different cities.

// creating the algorithm instance
var dijkstra = 
    new DijkstraShortestPathAlgorithm<int,Edge<int>>(cities, cityDistances);

// creating the observer
var vis = new VertexPredecessorRecorderObserver<int,Edge<int>>();
    
// compute and record shortest paths
using(ObserverScope.Create(dijkstra, vis))
   dijkstra.Compute(sourceCity);

// vis can create all the shortest path in the graph
foreach(var e in vis.Path(targetCity))
   Console.WriteLine(e);