/// <summary>
/// Create an arbitrary matching on the subset of vertices ('s') of provided
/// graph. The provided matching should be empty.
///
/// <param name="g">graph to match</param>
/// <param name="m">empty matching (presumed)</param>
/// <param name="s">subset of vertices</param>
/// <returns>number of vertices matched</returns>
/// </summary>
public static int Initial(Graph g, Matching m, BitArray s)
{
int nMatched = 0;
for (int v = BitArrays.NextSetBit(s, 0); v >= 0; v = BitArrays.NextSetBit(s, v + 1))
{
// skip if already matched
if (m.Matched(v))
{
continue;
}
// find a single edge which is not matched and match it
int d = g.Degree(v);
for (int j = 0; j < d; ++j)
{
Edge e = g.EdgeAt(v, j);
int w = e.Other(v);
if ((e.Bond != Bond.Single) && m.Unmatched(w) && s[w])
{
m.Match(v, w);
nMatched += 2;
break;
}
}
}
return(nMatched);
}
/// <summary>
/// When precisely two vertices are unmatched we only need to find a single
/// augmenting path. Rather than run through edmonds with blossoms etc we
/// simple do a targest DFS for the path.
///
/// <param name="g">graph</param>
/// <param name="m">matching</param>
/// <param name="nMatched">current matching cardinality must be |s|-nMathced == 2</param>
/// <param name="s">subset size</param>
/// <returns>new match cardinality</returns>
/// </summary>
public static int AugmentOnce(Graph g, Matching m, int nMatched, BitArray s)
{
int vStart = BitArrays.NextSetBit(s, 0);
while (vStart >= 0)
{
if (!m.Matched(vStart))
{
break;
}
vStart = BitArrays.NextSetBit(s, vStart + 1);
}
int vEnd = BitArrays.NextSetBit(s, vStart + 1);
while (vEnd >= 0)
{
if (!m.Matched(vEnd))
{
break;
}
vEnd = BitArrays.NextSetBit(s, vEnd + 1);
}
// find an augmenting path between vStart and vEnd
int[] path = new int[g.Order];
int len = FindPath(g, vStart, vEnd, s, path, 0, m, false);
if (len > 0)
{
// augment
for (int i = 0; i < len; i += 2)
{
m.Match(path[i], path[i + 1]);
}
nMatched += 2;
}
return(nMatched);
}
public static int Dfs(Graph g, Matching m, BitArray s)
{
int nMatched = 0;
BitArray unvisited = (BitArray)s.Clone();
// visit those with degree 1 first and expand out matching
for (int v = BitArrays.NextSetBit(unvisited, 0); v >= 0; v = BitArrays.NextSetBit(unvisited, v + 1))
{
if (!m.Matched(v))
{
int cnt = 0;
int d = g.Degree(v);
while (--d >= 0)
{
int w = g.EdgeAt(v, d).Other(v);
if (unvisited[w])
{
++cnt;
}
}
if (cnt == 1)
{
nMatched += DfsVisit(g, v, m, unvisited, true);
}
}
}
// now those which aren't degree 1
for (int v = BitArrays.NextSetBit(unvisited, 0); v >= 0; v = BitArrays.NextSetBit(unvisited, v + 1))
{
if (!m.Matched(v))
{
nMatched += DfsVisit(g, v, m, unvisited, true);
}
}
return(nMatched);
}