/// <summary>
/// Attempts to break cycles in the graph by removing the deepest remove edge, as defined
/// by the supplied predicate function.
/// </summary>
/// <param name="graph">The bidirectional graph to be processed.</param>
/// <param name="isRemovable">A function indicating whether or not a particular edge can be removed (i.e. is a "soft" dependency).</param>
/// <typeparam name="TVertex">The <see cref="Type" /> of the vertices of the graph.</typeparam>
/// <typeparam name="TEdge">The <see cref="Type" /> of the edges of the graph.</typeparam>
/// <returns>The list of edges that were removed to break the cycle(s).</returns>
/// <exception cref="NonAcyclicGraphException">Occurs if one or more of the cycles present in the graph cannot be broken by removing one of its edges.</exception>
public static IReadOnlyList <TEdge> BreakCycles <TVertex, TEdge>(this BidirectionalGraph <TVertex, TEdge> graph, Func <TEdge, bool> isRemovable)
where TEdge : IEdge <TVertex>
{
var removedEdges = new List <TEdge>();
// Get cyclical dependencies found in the graph
var cycles = graph.GetCycles();
// Break circular dependencies
foreach (var cycle in cycles)
{
// Last element of Path repeats first element (so ignore duplicate)
var distinctPathVertices = cycle.Path.Take(cycle.Path.Count - 1).ToArray();
var sacrificialDependency = distinctPathVertices
.Select(
(e, i) =>
{
// Get the next entity in the path (circling around to the first entity on the last item)
var dependentVertex = distinctPathVertices[(i + 1) % distinctPathVertices.Length];
return(new
{
DependentVertex = dependentVertex,
CycleEdges = graph.InEdges(dependentVertex).Where(IsCycleEdge)
});
})
.Reverse()
.FirstOrDefault(x => x.CycleEdges.All(isRemovable));
if (sacrificialDependency == null)
{
graph.ValidateGraph();
// Should never get here in this situation, but throw an exception to satisfy code analysis warnings
throw new NonAcyclicGraphException();
}
// Remove the chosen graph edge(s) to break the cyclical dependency
foreach (TEdge edge in sacrificialDependency.CycleEdges.ToArray())
{
if (_logger.IsDebugEnabled)
{
_logger.Debug($"Edge '{edge.ToString()}' removed to prevent the following cycle: {string.Join(" --> ", cycle.Path.Select(x => x.ToString()))}");
}
graph.RemoveEdge(edge);
removedEdges.Add(edge);
}
bool IsCycleEdge(TEdge edge) => distinctPathVertices.Contains(edge.Source);
}
if (_logger.IsDebugEnabled)
{
_logger.Debug($@"The following edges were removed from the graph to prevent cycles:
{string.Join(Environment.NewLine, removedEdges.Select(x => x.ToString()))}");
}
return(removedEdges);
}
