/// <summary>
/// Attempts to remove an edge entering a specific vertex from the strongly connected
/// portion of a specific connected subgraph and replace it with another edge towards an
/// edge from a weakly connected portion of the connected subgraph, thus expanding the
/// strongly connected portion.
/// </summary>
/// <param name="connectedSubgraph">The connected subgraph which contains a weakly
/// connected portion.</param>
/// <param name="vertex">The vertex from the strongly connected portion of the connected
/// subgraph.</param>
/// <returns><see langword="true"/> if the edge was successfully added.</returns>
private bool AddStronglyConnectingEdgeEnteringVertex(
ConnectedSubgraph connectedSubgraph,
Vertex vertex)
{
Vertex otherVertex = null;
List<Vertex> adjacentVertices = GetAdjacentVertices(vertex);
while (adjacentVertices.Count > 0)
{
int vertexIndex = _random.Next(adjacentVertices.Count);
Vertex adjacentVertex = adjacentVertices[vertexIndex];
if (!vertex.IsConnectedToVertex(adjacentVertex)
&& connectedSubgraph.ContainsVertex(adjacentVertex)
&& !connectedSubgraph.IsVertexStronglyConnected(adjacentVertex))
{
if (connectedSubgraph.CheckWillConnectStrongly(vertex, adjacentVertex))
{
if (!CheckCanConnectVertices(vertex, adjacentVertex))
{
// If the two vertices cannot be connected without causing an
// intersection, remove the other edge
Vertex crossVertex1 = _levelMatrix[vertex.Row, adjacentVertex.Column];
Vertex crossVertex2 = _levelMatrix[adjacentVertex.Row, vertex.Column];
RemoveEdgeBetweenVertices(crossVertex1, crossVertex2);
}
// Check if the other vertex has the maximum number of edges entering it
// and if so, remove a random edge entering it
if (adjacentVertex.ConnectedVertexCount == _maxEdges)
RemoveEdgeEnteringVertex(adjacentVertex);
otherVertex = adjacentVertex;
break;
}
}
adjacentVertices.RemoveAt(vertexIndex);
}
// If no suitable other vertex was found, give up
if (otherVertex == null)
return false;
// Check if the specified vertex has the maximum number of edges entering it and if so,
// remove a random edge entering it
if (vertex.ConnectedVertexCount == _maxEdges)
RemoveEdgeEnteringVertex(vertex);
// Add the edge to the level graph
AddEdgeBetweenVertices(vertex, otherVertex);
return true;
}
/// <summary>
/// Checks if an edge can be added between two adjacent vertices without resulting in an
/// intersection.
/// </summary>
/// <param name="vertex1">The first vertex.</param>
/// <param name="vertex2">The second vertex.</param>
/// <returns><see langword="true"/> if the vertices are not directly connected and an edge
/// can be added between them without resulting in an intersection.</returns>
private bool CheckCanConnectVertices(Vertex vertex1, Vertex vertex2)
{
// If the two vertices are already connected, they should not be connected again
if (vertex1.IsConnectedToVertex(vertex2))
return false;
// If the two vertices are diagonally adjacent in the level matrix, check if there is
// an edge between their opposite vertices that will result in an intersection
if (vertex1.Row != vertex2.Row && vertex1.Column != vertex2.Column)
{
Vertex crossVertex1 = _levelMatrix[vertex1.Row, vertex2.Column];
Vertex crossVertex2 = _levelMatrix[vertex2.Row, vertex1.Column];
if (crossVertex1.IsConnectedToVertex(crossVertex2))
return false;
}
return true;
}
/// <summary>
/// Attempts to add an edge entering an isolated vertex in order to meet the minimum
/// requirement of two edges entering it.
/// </summary>
/// <param name="vertex">The isolated vertex which needs another edge entering it.</param>
/// <returns><see langword="true"/> if the edge was successfully added.</returns>
private bool AddSecondaryEdgeEnteringVertex(Vertex vertex)
{
// Attempt to find an adjacent vertex that can be connected to the specified vertex; if
// an edge prevents the two vertices from being connected, remove it
Vertex otherVertex = null;
List<Vertex> adjacentVertices = GetAdjacentVertices(vertex);
while (adjacentVertices.Count > 0)
{
int vertexIndex = _random.Next(adjacentVertices.Count);
Vertex adjacentVertex = adjacentVertices[vertexIndex];
if (!vertex.IsConnectedToVertex(adjacentVertex))
{
if (!CheckCanConnectVertices(vertex, adjacentVertex))
{
// If the two vertices cannot be connected without causing an intersection,
// remove the other edge
Vertex crossVertex1 = _levelMatrix[vertex.Row, adjacentVertex.Column];
Vertex crossVertex2 = _levelMatrix[adjacentVertex.Row, vertex.Column];
RemoveEdgeBetweenVertices(crossVertex1, crossVertex2);
}
// Check if the other vertex has the maximum number of edges entering it and if
// so, remove a random edge entering it
if (adjacentVertex.ConnectedVertexCount == _maxEdges)
RemoveEdgeEnteringVertex(adjacentVertex);
otherVertex = adjacentVertex;
break;
}
adjacentVertices.RemoveAt(vertexIndex);
}
// If no suitable other vertex was found, give up
if (otherVertex == null)
return false;
// Add the edge to the level graph
AddEdgeBetweenVertices(vertex, otherVertex);
return true;
}
