/// <summary>
/// Merges the node x into the fixed target node into.
///
/// Edges between these nodes, edges to x and related distance information is updated.
///
/// x is marked as to be removed from the search space. If x was the start node, into
/// will now be the start node.
/// </summary>
/// <returns>All neighbors of x before merging. These are the nodes that had their adjacency
/// information changed.</returns>
protected IEnumerable <int> MergeInto(int x, int into)
{
if (!NodeStates.IsFixedTarget(into))
{
throw new ArgumentException("Nodes can only be merged into fixed target nodes", "into");
}
_data.DistanceLookup.IndexToNode(into).MergeWith(_data.DistanceLookup.IndexToNode(x), _data.DistanceLookup.GetShortestPath(x, into));
_data.DistanceLookup.MergeInto(x, into);
EdgeSet.Remove(x, into);
var intoNeighbors = EdgeSet.NeighborsOf(into);
var xNeighbors = EdgeSet.NeighborsOf(x);
var neighbors = intoNeighbors.Union(xNeighbors);
foreach (var neighbor in xNeighbors)
{
EdgeSet.Remove(x, neighbor);
}
foreach (var neighbor in neighbors)
{
EdgeSet.Add(into, neighbor, _data.DistanceLookup[into, neighbor]);
}
if (StartNodeIndex == x)
{
_data.StartNodeIndex = into;
}
NodeStates.MarkNodeAsRemoved(x);
return(xNeighbors);
}
protected override int ExecuteTest()
{
// The test only makes sense with at least 2 terminals.
if (NodeStates.FixedTargetNodeCount <= 1)
{
return(0);
}
var removedNodes = 0;
var untested = new HashSet <int>(NodeStates.FixedTargetNodeIndices);
// For each terminal z with degree of at least 2
while (untested.Any())
{
var z = untested.First();
untested.Remove(z);
var neighbors = EdgeSet.NeighborsOf(z);
if (neighbors.Count < 2)
{
continue;
}
// Determine the shortest and second shortest edge incident to z.
// For the second shortest, only the weight is of interest.
var tuple = ShortestTwoEdgesOf(EdgeSet.EdgesOf(z));
var shortest = tuple.Item1;
var secondShortestWeight = tuple.Item2;
// v is the node which is connected to z via the shortest edge.
var v = shortest.N1 == z ? shortest.N2 : shortest.N1;
// The shortest edge belongs to at least one Steiner minimal tree, if
// secondShortestWeight >= shortest.Weight + distance(v, y) for any terminal y, y != z
var canBeContracted = NodeStates.FixedTargetNodeIndices
.Where(y => z != y)
.Any(y => secondShortestWeight >= shortest.Weight + DistanceLookup[v, y]);
// If such a y exists, we can merge v into z.
if (canBeContracted)
{
// z was changed and can be tested again.
untested.Add(z);
// v no longer exists and as such must not be tested.
untested.Remove(v);
MergeInto(v, z);
removedNodes++;
}
}
return(removedNodes);
}
private void RemoveNode(int index)
{
if (NodeStates.IsTarget(index))
{
throw new ArgumentException("Target nodes can't be removed", "index");
}
var neighbors = EdgeSet.NeighborsOf(index);
switch (neighbors.Count)
{
case 0:
break;
case 1:
EdgeSet.Remove(index, neighbors[0]);
break;
case 2:
// Merge the two incident edges.
var left = neighbors[0];
var right = neighbors[1];
var newWeight = EdgeSet[index, left].Weight + EdgeSet[index, right].Weight;
EdgeSet.Remove(index, left);
EdgeSet.Remove(index, right);
if (newWeight <= DistanceLookup[left, right])
{
EdgeSet.Add(left, right, newWeight);
}
break;
default:
throw new ArgumentException("Removing nodes with more than 2 neighbors is not supported", "index");
}
NodeStates.MarkNodeAsRemoved(index);
}
protected override int ExecuteTest()
{
var edges = new GraphEdge[SearchSpaceSize];
var removedNodes = 0;
for (var i = 0; i < SearchSpaceSize; i++)
{
// This test only checks non-terminals.
if (NodeStates.IsTarget(i))
{
continue;
}
// Nodes with less than 3 neighbors are covered by DegreeTest
// Nodes are limited to 7 neighbors because this test is exponential in the neighbor count.
var neighbors = EdgeSet.NeighborsOf(i);
if (neighbors.Count < 3 || neighbors.Count > 7)
{
continue;
}
// Cache the edges. They might be removed from EdgeSet when we need them.
foreach (var neighbor in neighbors)
{
edges[neighbor] = EdgeSet[i, neighbor];
}
// Check whether each subset satisfies the condition.
var canBeRemoved = true;
foreach (var subset in GetAllSubsets(neighbors))
{
// Only subsets of at least size 3 are relevant.
if (subset.Count < 3)
{
continue;
}
// Sum up the weights of all edges between the nodes of the subsets and i.
var edgeSum = subset.Sum(j => edges[j].Weight);
// Build the MST of the fully connected graph of the nodes in the subset with the bottleneck
// Steiner distances as edge weights.
var mst = new MinimalSpanningTree(subset, SMatrix);
mst.Span(subset[0]);
// Sum up the edge weights of the MST.
var mstSum = mst.SpanningEdges.Sum(e => e.Priority);
// The condition is only satisfied if edgeSum >= mstSum.
if (edgeSum < mstSum)
{
canBeRemoved = false;
break;
}
}
if (!canBeRemoved)
{
continue;
}
// Remove i and replace its edges.
foreach (var neighbor in neighbors)
{
// Remove the old edges between i and its neighbors.
var edge = edges[neighbor];
EdgeSet.Remove(edge);
// For each pair of neighbors create a new edge.
foreach (var neighbor2 in neighbors)
{
if (neighbor >= neighbor2)
{
continue;
}
// The weight of the new edge between the two neighbors is the sum of their edge weights to i.
var edge2 = edges[neighbor2];
var newEdgeWeight = edge.Weight + edge2.Weight;
// Only add this edge if it wouldn't be removed by the Paths with many terminals test.
if (newEdgeWeight <= SMatrix[neighbor, neighbor2])
{
EdgeSet.Add(neighbor, neighbor2, newEdgeWeight);
}
}
}
NodeStates.MarkNodeAsRemoved(i);
removedNodes++;
}
return(removedNodes);
}
protected override int ExecuteTest()
{
var removedNodes = 0;
var untested = new HashSet <int>(Enumerable.Range(0, SearchSpaceSize));
var dependentNodes = new Dictionary <int, List <int> >();
while (untested.Any())
{
var i = untested.First();
untested.Remove(i);
var neighbors = EdgeSet.NeighborsOf(i);
if (!NodeStates.IsTarget(i))
{
if (neighbors.Count == 1)
{
// Non target nodes with one neighbor can be removed.
untested.Add(neighbors[0]);
RemoveNode(i);
removedNodes++;
}
else if (neighbors.Count == 2)
{
// Non target nodes with two neighbors can be removed and their neighbors
// connected directly.
untested.Add(neighbors[0]);
untested.Add(neighbors[1]);
RemoveNode(i);
removedNodes++;
}
}
else if (NodeStates.IsFixedTarget(i))
{
if (neighbors.Count == 1)
{
var other = neighbors[0];
if (EdgeSet.NeighborsOf(other).Count > 2 || NodeStates.IsTarget(other))
{
// Fixed target nodes with one neighbor can be merged with their neighbor since
// it must always be taken.
untested.Add(i);
untested.Remove(other);
untested.UnionWith(MergeInto(other, i));
removedNodes++;
}
else
{
// Node can only be merged once other has been processed. Other might be a dead end.
Debug.Assert(untested.Contains(other));
dependentNodes.Add(other, i);
}
}
else if (neighbors.Count > 1)
{
// Edges from one target node to another that are of minimum cost among the edges of
// one of the nodes can be in any optimal solution. Therefore both target nodes can be merged.
var minimumEdgeCost = neighbors.Min(other => DistanceLookup[i, other]);
var minimumTargetNeighbors =
neighbors.Where(other => DistanceLookup[i, other] == minimumEdgeCost && NodeStates.IsFixedTarget(other));
foreach (var other in minimumTargetNeighbors)
{
untested.Add(i);
untested.Remove(other);
untested.UnionWith(MergeInto(other, i));
removedNodes++;
}
}
}
List <int> dependent;
if (dependentNodes.TryGetValue(i, out dependent))
{
untested.UnionWith(dependent);
}
}
return(removedNodes);
}
protected override int ExecuteTest()
{
var removedNodes = 0;
var untested = new HashSet <int>(Enumerable.Range(0, SearchSpaceSize));
while (untested.Any())
{
var i = untested.First();
untested.Remove(i);
var neighbors = EdgeSet.NeighborsOf(i);
if (!NodeStates.IsTarget(i))
{
if (neighbors.Count == 1)
{
// Non target nodes with one neighbor can be removed.
untested.Add(neighbors[0]);
RemoveNode(i);
removedNodes++;
}
else if (neighbors.Count == 2)
{
// Non target nodes with two neighbors can be removed and their neighbors
// connected directly.
untested.Add(neighbors[0]);
untested.Add(neighbors[1]);
RemoveNode(i);
removedNodes++;
}
}
else if (NodeStates.IsFixedTarget(i))
{
if (neighbors.Count == 1)
{
var other = neighbors[0];
// Fixed target nodes with one neighbor can be merged with their neighbor since
// it must always be taken.
// If the neighbor is no target and of degree 1 or 2, it will be removed by the tests above,
// after which this node will be processed again.
if (EdgeSet.NeighborsOf(other).Count <= 2 && !NodeStates.IsTarget(other))
{
continue;
}
// If this node is the only fixed target, the neighbor must not be merged because
// if this is the only target, the neighbor and the rest of the tree will not be in the optimal solution,
// if there are only variable target nodes, the neighbor will not be in the optimal solution if the variable nodes are not taken.
if (NodeStates.FixedTargetNodeCount == 1)
{
continue;
}
untested.Add(i);
untested.Remove(other);
untested.UnionWith(MergeInto(other, i));
removedNodes++;
}
else if (neighbors.Count > 1)
{
// Edges from one target node to another that are of minimum cost among the edges of
// one of the nodes can be in any optimal solution. Therefore both target nodes can be merged.
var minimumEdgeCost = neighbors.Min(other => DistanceLookup[i, other]);
var minimumTargetNeighbors =
neighbors.Where(other => DistanceLookup[i, other] == minimumEdgeCost && NodeStates.IsFixedTarget(other));
foreach (var other in minimumTargetNeighbors)
{
untested.Add(i);
untested.Remove(other);
untested.UnionWith(MergeInto(other, i));
removedNodes++;
}
}
}
}
return(removedNodes);
}