/// <summary>
/// Single-source multiple-target version of Dijkstra's shortest path algorithm that returns shortest paths to a specified number of targets.
/// </summary>
/// <param name="source">Source vertex to start searching from.</param>
/// <param name="targets">Target vertices to find shortest paths to.</param>
/// <param name="count">Number of targets to find.</param>
/// <returns>Mapping of all shortest paths from the source to all vertices up to <paramref name="count"/> targets.</returns>
/// <remarks>
/// The graph attached to <paramref name="source"/> should not contain any negative cycles.
/// </remarks>
public static IDictionary<IVertex, Path> ShortestPaths(IVertex source, ICollection<IVertex> targets, int count)
{
if (source == null)
throw new ArgumentNullException("source");
if (targets == null)
throw new ArgumentNullException("targets");
if (count < 1)
throw new ArgumentOutOfRangeException("count");
// Create a priority queue where target vertices are prioritized by shortest path weight, starting with the source.
PriorityQueue<IVertex, int> queue = new PriorityQueue<IVertex, int>();
IDictionary<IVertex, IEdge/*?*/> edges = new Dictionary<IVertex, IEdge/*?*/>();
// Initialize the source with a path of 0 length.
queue[source] = 0;
edges[source] = null;
// Keep track of the explored vertices with known minimal length.
IDictionary<IVertex, Path> shortestPaths = new Dictionary<IVertex, Path>();
// The number of explored targets.
int targetsFound = 0;
// Keep track of the upper bound on the distance to the closest 'count' nodes.
// See "A Heuristic for Dijkstra's Algorithm" for details.
PriorityQueue<IVertex, int> bounds = new PriorityQueue<IVertex, int>(true);
foreach (IVertex target in targets)
{
bounds.Enqueue(target, int.MaxValue);
if (bounds.Count == count)
break;
}
// Traverse the queue.
while (queue.Count > 0)
{
// Get the next closest vertex and copy it to the list of shortest paths.
KeyValuePair<IVertex, int> item = queue.Dequeue();
source = item.Key;
// We've found the shortest path to this vertex.
IEdge/*?*/ shortest = edges[source];
if (shortest == null)
shortestPaths[source] = new Path(source);
else
shortestPaths[source] = shortestPaths[shortest.Source] + shortest;
// If we've explored the requested number of targets then break early.
if (targets.Contains(source))
if (++targetsFound >= count)
break;
// Relax all outgoing edges from this vertex.
foreach (IEdge edge in source.Edges)
{
// If we haven't explored the target yet.
IVertex target = edge.Target;
if (!shortestPaths.ContainsKey(target))
{
// Calculate the new cost via this edge.
int newCost = item.Value + edge.Cost;
// Only relax the edge if the cost is an improvement (i.e. less than) the shortest paths seen so far.
// See "A Heuristic for Dijkstra's Algorithm" for details.
if (newCost < bounds.Peek().Value)
{
// Compare the new path with the current paths.
int currentCost;
if (!queue.TryGetValue(target, out currentCost) || newCost < currentCost)
{
// If no current path exists or the new path is shorter, then update the shortest path in the queue.
queue[target] = newCost;
edges[target] = edge;
// If the target is a final target then update the cost in the list of upper bounds.
if (targets.Contains(target))
{
bounds[target] = newCost;
// We only need to keep track of the closest 'count' targets.
if (bounds.Count > count)
bounds.Dequeue();
}
}
}
}
}
}
return shortestPaths;
}
