/// <summary>
/// Add a match to the isomorphism
/// </summary>
/// <remarks>
/// This is only a proposed match. If it fails, the passed in BacktrackRecord
/// will have all the actions taken as a consequence and they can be undone using
/// that BacktrackRecord.
/// </remarks>
/// <param name="mtc">Proposed match</param>
/// <param name="btr">BacktrackRecord to record actions into</param>
/// <returns>True if match is locally consistent with a full isomorphism</returns>
private bool FAddMatchToSolution(Match mtc, BacktrackRecord <TV, TE> btr)
{
var ivtx1 = mtc.Ivtx1;
var ivtx2 = mtc.Ivtx2;
// Record the match action in the backtrackRecord
btr.SetMatch(mtc.Ivtx1, mtc.Ivtx2, this);
// In and Out neighbors of the vertices in the match
var lstIn1 = VfGraph1.InNeighbors(ivtx1);
var lstIn2 = VfGraph2.InNeighbors(ivtx2);
var lstOut1 = VfGraph1.OutNeighbors(ivtx1);
var lstOut2 = VfGraph2.OutNeighbors(ivtx2);
// Reclassify any neighbors of the added vertices that require it
foreach (var ivtx in lstOut1)
{
if (((int)VfGraph1.GetGroup(ivtx) & (int)(Group.Disconnected | Group.ToMapping)) != 0)
{
btr.MoveToGroup(1, ivtx, Group.FromMapping, this);
}
}
foreach (var ivtx in lstIn1)
{
if (((int)VfGraph1.GetGroup(ivtx) & (int)(Group.Disconnected | Group.FromMapping)) != 0)
{
btr.MoveToGroup(1, ivtx, Group.ToMapping, this);
}
}
foreach (var ivtx in lstOut2)
{
if (((int)VfGraph2.GetGroup(ivtx) & (int)(Group.Disconnected | Group.ToMapping)) != 0)
{
btr.MoveToGroup(2, ivtx, Group.FromMapping, this);
}
}
foreach (var ivtx in lstIn2)
{
if (((int)VfGraph2.GetGroup(ivtx) & (int)(Group.Disconnected | Group.FromMapping)) != 0)
{
btr.MoveToGroup(2, ivtx, Group.ToMapping, this);
}
}
// If the total degrees into or out of the isomorphism don't match up properly (less for
// subgraph isomorphism equal for exact isomorphism) then we can never match properly.
if (!FnCompareDegrees(_outDegreeTotal1, _outDegreeTotal2) ||
!FnCompareDegrees(_inDegreeTotal1, _inDegreeTotal2))
{
return(false);
}
// Also check the vertex counts which is a different check from the total degree above...
return(FnCompareDegrees(lstOut1.Count, lstOut2.Count) && FnCompareDegrees(lstIn1.Count, lstIn2.Count));
}
/// <summary>
/// Determine if a match is feasible or not
/// </summary>
/// <remarks>
/// This is the heart of the VF isomorphism algorithm.
/// </remarks>
/// <param name="mtc">Match to check</param>
/// <returns>True if feasible, False if not</returns>
private bool FFeasible(Match mtc)
{
var ivtx1 = mtc.Ivtx1;
var ivtx2 = mtc.Ivtx2;
// Allow the user to override with a context check on the matching.
if (_fContextCheck)
{
var icc1 = VfGraph1.GetAttr(ivtx1) as IContextCheck;
var icc2 = VfGraph2.GetAttr(ivtx2) as IContextCheck;
if (icc1 != null && icc2 != null)
{
if (!icc1.FCompatible(icc2))
{
// User says they're not compatible regardless of the topology
return(false);
}
}
}
var lstIn1 = VfGraph1.InNeighbors(ivtx1);
var lstIn2 = VfGraph2.InNeighbors(ivtx2);
var lstOut1 = VfGraph1.OutNeighbors(ivtx1);
var lstOut2 = VfGraph2.OutNeighbors(ivtx2);
// Vertex1's In Neighbors in mapping must map to Vertex2's In Neighbors...
if (!FLocallyIsomorphic(lstIn1, lstIn2))
{
return(false);
}
// Ditto the above for out neighbors...
if (!FLocallyIsomorphic(lstOut1, lstOut2))
{
return(false);
}
// Verify the in, out and new predicate from the paper. This amounts to
// checking that the counts for the group classifications in the corresponding
// lists below must match.
if (!FInOutNew(lstOut1, lstIn1, lstOut2, lstIn2))
{
return(false);
}
return(true);
}
/// <summary>
/// Ensure that degrees of vertices are compatible
/// </summary>
/// <returns>True if compatible, False if not</returns>
private bool FCompatibleDegrees()
{
if (!FnCompareDegrees(VfGraph1.VertexCount, VfGraph2.VertexCount))
{
return(false);
}
// Since we've sorted the vertices by degree, we can do a quick compare on the degree sequence
// on a vertex by vertex basis...
for (var iVertex = 0; iVertex < VfGraph2.VertexCount; iVertex++)
{
if (!FnCompareDegrees(VfGraph1.TotalDegree(iVertex), VfGraph2.TotalDegree(iVertex)))
{
return(false);
}
}
return(true);
}
