public static int Dijkstra(Vertex from, Vertex to, Graph graph)
{
HashSet<Vertex> visited = new HashSet<Vertex>();
Dictionary<Vertex, FibonacciHeap<int, Vertex>.Node> nodes = new Dictionary<Vertex, FibonacciHeap<int, Vertex>.Node>();
FibonacciHeap<int, Vertex> labels = new FibonacciHeap<int, Vertex>();
// Initialize labels.
foreach (var vertex in graph.Vertices)
{
var n = labels.Add(vertex == from ? 0 : int.MaxValue, vertex);
nodes.Add(vertex, n);
}
int currentLabel = int.MaxValue;
while (!visited.Contains(to))
{
var currentNode = labels.ExtractMin();
var current = currentNode.Value;
currentLabel = currentNode.Key;
// Consider all edges ending in unvisited neighbours
var edges =
graph.GetEdgesForVertex(current).Where(x => !visited.Contains(x.Other(current)));
// Update labels on the other end.
foreach (var edge in edges)
{
if (currentNode.Key + edge.Cost < nodes[edge.Other(current)].Key)
labels.DecreaseKey(nodes[edge.Other(current)], currentNode.Key + edge.Cost);
}
visited.Add(current);
}
return currentLabel;
}
private Graph(int nbVertices)
: this()
{
_vertices = new HashSet<Vertex>();
Vertices = new List<Vertex>(nbVertices);
// Create the vertices
for (int i = 0; i < nbVertices; i++)
{
var v = new Vertex(i + 1); //Start counting at 1.
AddVertex(v);
}
}
public static Path DijkstraPath(Vertex from, Vertex to, Graph graph)
{
HashSet<Vertex> visited = new HashSet<Vertex>();
Dictionary<Vertex, FibonacciHeap<int, Vertex>.Node> nodes =
new Dictionary<Vertex, FibonacciHeap<int, Vertex>.Node>();
Dictionary<Vertex, Edge> comingFrom = new Dictionary<Vertex, Edge>();
FibonacciHeap<int, Vertex> labels = new FibonacciHeap<int, Vertex>();
// Initialize labels.
foreach (var vertex in graph.Vertices)
{
var n = labels.Add(vertex == from ? 0 : int.MaxValue, vertex);
nodes.Add(vertex, n);
comingFrom.Add(vertex, null);
}
while (!visited.Contains(to))
{
var currentNode = labels.ExtractMin();
var current = currentNode.Value;
// Consider all edges ending in unvisited neighbours
var edges =
graph.GetEdgesForVertex(current).Where(x => !visited.Contains(x.Other(current)));
// Update labels on the other end.
foreach (var edge in edges)
{
if (currentNode.Key + edge.Cost < nodes[edge.Other(current)].Key)
{
labels.DecreaseKey(nodes[edge.Other(current)], currentNode.Key + edge.Cost);
comingFrom[edge.Other(current)] = edge;
}
}
visited.Add(current);
}
// Now travel back, to find the actual path
List<Edge> pathEdges = new List<Edge>();
Vertex pathVertex = to;
while (pathVertex != from)
{
pathEdges.Add(comingFrom[pathVertex]);
pathVertex = comingFrom[pathVertex].Other(pathVertex);
}
pathEdges.Reverse();
Path path = new Path(from);
path.Edges.AddRange(pathEdges);
return path;
}
public Graph RemoveVertexAndReconnect(Graph currentSolution, Graph problemInstance, Vertex remove)
{
var workingSolution = currentSolution.Clone();
foreach (var vertex in problemInstance.Vertices)
if (!workingSolution.ContainsVertex(vertex))
workingSolution.AddVertex(vertex);
foreach (var edge in workingSolution.GetEdgesForVertex(remove).ToList())
workingSolution.RemoveEdge(edge);
IEnumerable<Vertex> degreeOne;
while ((degreeOne =
workingSolution.Vertices.Except(problemInstance.Terminals)
.Where(x => workingSolution.GetDegree(x) == 1)).Any())
{
foreach (var degreeZeroSteiner in degreeOne.ToList())
foreach (var edge in workingSolution.GetEdgesForVertex(degreeZeroSteiner).ToList())
workingSolution.RemoveEdge(edge, false);
}
ReconnectTerminals(workingSolution, problemInstance);
return workingSolution;
}
public static IEnumerable<IEnumerable<Vertex>> BFS(Graph graph, HashSet<Vertex> visited, Vertex end, Vertex expand)
{
if (graph.Terminals.All(visited.Contains) || visited.Count == graph.NumberOfVertices - 1)
yield break;
List<Vertex> nodes = graph.GetNeighboursForVertex(expand);
//for (int i = 0; i < nodes.Count; i++ )
//{
// foreach (var combination in new Combinations<Vertex>(nodes, i + 1))
// {
// if (combination.Any(x => visited.Contains(x)))
// continue;
// if (combination.Contains(end))
// {
// foreach (var n in combination)
// visited.Add(n);
// foreach (var n in combination)
// foreach (var bfs in BFS(graph, visited, end, n))
// yield return bfs;
// foreach (var n in combination)
// visited.Remove(n);
// break;
// }
// }
//}
foreach (var node in nodes)
{
if (visited.Contains(node))
continue;
if (node == end)
{
visited.Add(node);
yield return visited;
visited.Remove(node);
break;
}
}
//for (int i = 0; i < nodes.Count; i++)
//{
// if (visited.Count + i == graph.NumberOfVertices - 1)
// break; // Adding i+1 results in all nodes, which is useless.
// foreach (var combination in new Combinations<Vertex>(nodes, i + 1))
// {
// if (combination.Any(visited.Contains)) // || combination.Contains(end))
// continue;
// foreach (var n in combination)
// visited.Add(n);
// foreach (var n in combination)
// foreach (var bfs in BFS(graph, visited, end, n))
// yield return bfs;
// foreach (var n in combination)
// visited.Remove(n);
// }
//}
foreach (var node in nodes)
{
if (visited.Contains(node) || node == end)
continue;
visited.Add(node);
foreach (var bfs in BFS(graph, visited, end, node))
yield return bfs;
visited.Remove(node);
}
}
public int GetVoronoiRadiusForTerminal(Vertex vertex)
{
if (!Terminals.Contains(vertex))
throw new ArgumentException("The given vertex should be a terminal.");
if (_voronoiRadius.ContainsKey(vertex))
return _voronoiRadius[vertex];
ComputeVoronoiRegions();
return _voronoiRadius[vertex];
}
/// <summary>
/// Method to get the neighbours of a given vertex.
/// </summary>
/// <param name="v">The vertex of which to get all the neighbours.</param>
/// <returns>A list containing all the neighbours of the given vertex.</returns>
public List<Vertex> GetNeighboursForVertex(Vertex v)
{
if (_adjacencies.ContainsKey(v))
return _adjacencies[v].Select(x => x.Other(v)).ToList();
throw new ArgumentException("The given vertex is not in this graph.");
}
/// <summary>
/// Method to get the degree of a vertex in the graph.
/// </summary>
/// <param name="v">The vertex of which to get the degree.</param>
/// <returns>The degree of the given vertex.</returns>
public int GetDegree(Vertex v)
{
if (!_adjacencies.ContainsKey(v))
throw new ArgumentException("The given vertex v is not contained in this graph.");
return _adjacencies[v].Count;
}
/// <summary>
/// Method to check if the graph contains a given vertex in constant time.
/// </summary>
/// <param name="vertex"></param>
/// <returns>Boolean indicating whether the given vertex is present in the graph.</returns>
public bool ContainsVertex(Vertex vertex)
{
return _vertices.Contains(vertex);
}
/// <summary>
/// Method to peek at the next vertex to apply interleaving Dijkstra on.
/// </summary>
/// <returns>The vertex on which to apply interleaving Dijkstra next.</returns>
public Vertex PeekNextVertex()
{
// Find the next vertex
if (_currentlyLowestLabelUnusedVertex == null)
_currentlyLowestLabelUnusedVertex = GetLowestLabelUnusedVertex();
return _currentlyLowestLabelUnusedVertex;
}
/// <summary>
/// Method to get the next vertex to apply interleaving Dijkstra on.
/// </summary>
/// <returns>The vertex on which to apply interleaving Dijkstra.</returns>
public Vertex GetNextVertex()
{
// Find the next vertex
if (_currentlyLowestLabelUnusedVertex == null)
_currentlyLowestLabelUnusedVertex = GetLowestLabelUnusedVertex();
_currentlyUsingVertex = _currentlyLowestLabelUnusedVertex;
_currentlyLowestLabelUnusedVertex = null;
return _currentlyUsingVertex;
}
/// <summary>
/// Get the vertex of which the current Dijkstra procedure's lowest label is lowest of all procedures.
/// </summary>
/// <returns>The vertex for which the Dijkstra procedure currently has the lowest label.</returns>
public Vertex GetLowestLabelUnusedVertex()
{
if (_currentlyLowestLabelUnusedVertex != null)
return _currentlyLowestLabelUnusedVertex;
int value = int.MaxValue;
Vertex vertex = null;
foreach (var kvPair in _dictLabels)
{
if (kvPair.Key == _currentlyUsingVertex) continue;
var fibonacciHeap = kvPair.Value;
if (fibonacciHeap.IsEmpty()) continue;
var node = fibonacciHeap.Peek();
if (node.Key <= value)
{
vertex = kvPair.Key;
value = node.Key;
}
}
_currentlyLowestLabelUnusedVertex = vertex;
return _currentlyLowestLabelUnusedVertex;
}
public List<Path> FindPathsEndingInThisVertex(Vertex end)
{
List<Path> paths = new List<Path>();
foreach (var kvPair in _dictPathsfound)
{
var pathsDictionary = kvPair.Value;
if (pathsDictionary.ContainsKey(end))
paths.Add(pathsDictionary[end]);
}
return paths;
}
public void AddVertexToInterleavingDijkstra(Vertex vertex, Graph graph)
{
if (_verticesInSearch.Contains(vertex))
throw new InvalidOperationException("Can not add the vertex, because it is already added.");
_verticesInSearch.Add(vertex);
var labels = new FibonacciHeap<int, Vertex>();
var nodes = new Dictionary<Vertex, FibonacciHeap<int, Vertex>.Node>();
// Initialize labels.
foreach (var v in graph.Vertices)
{
var node = labels.Add(v == vertex ? 0 : int.MaxValue, v);
nodes.Add(v, node);
}
_dictLabels.Add(vertex, labels);
_dictNodes.Add(vertex, nodes);
_dictVisited.Add(vertex, new HashSet<Vertex>());
_dictPathsfound.Add(vertex, new Dictionary<Vertex, Path>());
_dictComingFrom.Add(vertex, new Dictionary<Vertex, Edge>());
_dictComponent.Add(vertex, ++_internalNewComponentCount); // All vertices start in a different component.
}
public static IEnumerable<IEnumerable<Vertex>> GetBFS(Graph graph, Vertex root)
{
yield return new[] { root };
foreach (var end in graph.Vertices.Except(new [] { root }))
{
HashSet<Vertex> visited = new HashSet<Vertex>();
visited.Add(root);
foreach (var bfs in BFS(graph, visited, end, root))
yield return bfs;
}
}
/// <summary>
/// Method to add an edge to the graph.
/// </summary>
/// <param name="from">Vertex from which the edge starts.</param>
/// <param name="to">Vertex at which the edge ends.</param>
/// <param name="cost">The cost of the edge.</param>
public void AddEdge(Vertex from, Vertex to, int cost)
{
var edge = new Edge(from, to, cost);
AddEdge(edge);
}
public void AddVertex(Vertex vertex)
{
if (_vertices.Contains(vertex))
return;
Vertices.Add(vertex);
_vertices.Add(vertex);
_adjacencies.Add(vertex, new List<Edge>());
_terminalDistance = null;
}
public static Dictionary<Vertex, Path> DijkstraPathToAll(Vertex from, Graph graph)
{
return DijkstraPathToAll(from, graph, false);
}
/// <summary>
/// Do a Depth First traversal on the graph, starting with a given vertex.
/// </summary>
/// <param name="start">The vertex from which to start the depth first traversal.</param>
/// <returns>A depth first traversal from the given start vertex.</returns>
public IEnumerable<Vertex> DepthFirstTraversal(Vertex start, bool ltr = true)
{
var visited = new HashSet<Vertex>();
var stack = new Stack<Vertex>();
stack.Push(start);
while (stack.Count != 0)
{
var current = stack.Pop();
if (!visited.Add(current))
continue;
yield return current;
var neighbours = this.GetNeighboursForVertex(current)
.Where(n => !visited.Contains(n));
foreach (var neighbour in ltr ? neighbours.Reverse() : neighbours)
stack.Push(neighbour);
}
}
public static Dictionary<Vertex, Path> DijkstraPathToAllTerminals(Vertex from, Graph graph)
{
return DijkstraPathToAll(from, graph, true);
}
/// <summary>
/// Method to get the edges that are connected to a given vertex.
/// </summary>
/// <param name="v">The vertex to get all the edges for.</param>
/// <returns>A list containing all the edges that the given vertex is connected to.</returns>
public List<Edge> GetEdgesForVertex(Vertex v)
{
if (_adjacencies.ContainsKey(v))
return _adjacencies[v];
throw new ArgumentException("The given vertex is not in this graph.");
}
public static Path NearestTerminal(Vertex from, Graph graph)
{
return NearestTerminals(from, graph, 1).FirstOrDefault();
}
/// <summary>
/// Method to get an IEnumerable with the non-terminal vertices in the Veronoi region of
/// a certain terminal.
/// </summary>
/// <param name="terminal">The terminal to determine the Veronoi region.</param>
/// <returns>List of non-terminals in the Veronoi region</returns>
public IEnumerable<Vertex> GetVerticesInVoronoiRegion(Vertex terminal)
{
foreach (var vertex in Vertices)
{
if (GetVoronoiRegionForVertex(vertex) == terminal)
yield return vertex;
}
}
public static List<Path> NearestTerminals(Vertex from, Graph graph, int n)
{
List<Path> foundPaths = new List<Path>();
HashSet<Vertex> visited = new HashSet<Vertex>();
Dictionary<Vertex, FibonacciHeap<int, Vertex>.Node> nodes = new Dictionary<Vertex, FibonacciHeap<int, Vertex>.Node>();
FibonacciHeap<int, Vertex> labels = new FibonacciHeap<int, Vertex>();
Dictionary<Vertex, Edge> comingFrom = new Dictionary<Vertex, Edge>();
if (graph.Terminals.Contains(from))
foundPaths.Add(new Path(from));
// Initialize labels.
foreach (var vertex in graph.Vertices)
{
var node = labels.Add(vertex == from ? 0 : int.MaxValue, vertex);
nodes.Add(vertex, node);
comingFrom.Add(vertex, null);
}
while (!labels.IsEmpty() && foundPaths.Count < n)
{
var currentNode = labels.ExtractMin();
var current = currentNode.Value;
// Consider all edges ending in unvisited neighbours
var edges =
graph.GetEdgesForVertex(current).Where(x => !visited.Contains(x.Other(current)));
// Update labels on the other end.
foreach (var edge in edges)
{
if (currentNode.Key + edge.Cost < nodes[edge.Other(current)].Key)
{
labels.DecreaseKey(nodes[edge.Other(current)], currentNode.Key + edge.Cost);
comingFrom[edge.Other(current)] = edge;
}
}
visited.Add(current);
if (graph.Terminals.Contains(current) && current != from)
{
// Now travel back, to find the actual path
List<Edge> pathEdges = new List<Edge>();
Vertex pathVertex = current;
while (pathVertex != from)
{
pathEdges.Add(comingFrom[pathVertex]);
pathVertex = comingFrom[pathVertex].Other(pathVertex);
}
pathEdges.Reverse();
Path path = new Path(from);
path.Edges.AddRange(pathEdges);
foundPaths.Add(path);
}
}
return foundPaths;
}
/// <summary>
/// Method to get the Terminal for which the given vertex belongs to its Veronoi region.
/// </summary>
/// <param name="vertex">The vertex for which to get the Veronoi region.</param>
/// <returns>The terminal in which the vertex is in the Veronoi region.</returns>
public Vertex GetVoronoiRegionForVertex(Vertex vertex)
{
if (Terminals.Contains(vertex))
return vertex;
if (_voronoiRegions.ContainsKey(vertex))
return _voronoiRegions[vertex];
ComputeVoronoiRegions();
return _voronoiRegions[vertex];
}
private static bool ExistsPath(Vertex v1, Vertex v2, Graph graph, List<Vertex> visited)
{
foreach (var edge in graph.GetEdgesForVertex(v1))
{
if (edge.Other(v1) == v2)
{
return true;
}
if (!visited.Contains(edge.Other(v1)))
{
var visited2 = visited.ToList();
visited2.Add(v1);
if (ExistsPath(edge.Other(v1), v2, graph, visited2))
return true;
}
}
return false;
}
/// <summary>
/// Method to remove a vertex from this graph.
/// Also removes all the edges that this vertex was connected to.
/// </summary>
/// <param name="vertex">The vertex to remove.</param>
public void RemoveVertex(Vertex vertex)
{
if (!_vertices.Contains(vertex))
return;
_vertices.Remove(vertex);
Vertices.Remove(vertex);
foreach (var edge in _adjacencies[vertex].ToList())
RemoveEdge(edge);
_terminalDistance = null;
_adjacencies.Remove(vertex);
}
public static Dictionary<Vertex, Path> DijkstraPathToAll(Vertex from, Graph graph, bool onlyTerminals)
{
Dictionary<Vertex, Edge> comingFrom = new Dictionary<Vertex, Edge>();
HashSet<Vertex> visited = new HashSet<Vertex>();
Dictionary<Vertex, FibonacciHeap<int, Vertex>.Node> nodes =
new Dictionary<Vertex, FibonacciHeap<int, Vertex>.Node>();
Dictionary<Vertex, Path> paths = new Dictionary<Vertex, Path>();
FibonacciHeap<int, Vertex> labels = new FibonacciHeap<int, Vertex>();
// Initialize labels.
foreach (var vertex in graph.Vertices)
{
var n = labels.Add(vertex == from ? 0 : int.MaxValue, vertex);
nodes.Add(vertex, n);
}
while (paths.Count < (onlyTerminals ? graph.Terminals.Count - 1 : graph.NumberOfVertices - 1))
{
var currentNode = labels.ExtractMin();
var current = currentNode.Value;
// Consider all edges ending in unvisited neighbours
var edges =
graph.GetEdgesForVertex(current).Where(x => !visited.Contains(x.Other(current)));
// Update labels on the other end.
foreach (var edge in edges)
{
if (currentNode.Key + edge.Cost < nodes[edge.Other(current)].Key)
{
labels.DecreaseKey(nodes[edge.Other(current)], currentNode.Key + edge.Cost);
comingFrom[edge.Other(current)] = edge;
}
}
visited.Add(current);
if (current != from && (!onlyTerminals || graph.Terminals.Contains(current)))
{
// Travel back the path
List<Edge> pathEdges = new List<Edge>();
Vertex pathVertex = current;
while (pathVertex != from)
{
pathEdges.Add(comingFrom[pathVertex]);
pathVertex = comingFrom[pathVertex].Other(pathVertex);
}
pathEdges.Reverse();
Path path = new Path(from);
path.Edges.AddRange(pathEdges);
paths[current] = path;
}
}
return paths;
}
public Path(Vertex start)
{
Edges = new List<Edge>();
Start = start;
}
public static IEnumerable<IEnumerable<Vertex>> GetAllConnectedCombinations(Graph graph, Vertex start)
{
var visited = new HashSet<Vertex>();
var terminals = new HashSet<Vertex>(graph.Terminals);
var stack = new Stack<Vertex>();
Dictionary<Vertex, Vertex> childParentDictionary = new Dictionary<Vertex, Vertex>();
stack.Push(start);
childParentDictionary.Add(start, null);
while (stack.Count != 0)
{
var current = stack.Pop();
if (!visited.Add(current))
continue;
var neighbours = graph.GetNeighboursForVertex(current)
.Where(n => !visited.Contains(n))
.ToList();
// Travel left to right
neighbours.Reverse();
foreach (var neighbour in neighbours)
{
stack.Push(neighbour);
childParentDictionary.Add(neighbour, current);
}
if (!neighbours.Any() || neighbours.All(visited.Contains))
{
List<Vertex> vertices = new List<Vertex>();
Vertex parentNode = current;
do
{
vertices.Add(parentNode);
} while ((parentNode = childParentDictionary[parentNode]) != null);
yield return vertices;
}
}
}
