public static Dictionary <PartialSolution, int> Reduce_M4R(Dictionary <PartialSolution, int> table, double tr)
{
// No point further reducing something empty
if (!table.Any() || table.First().Key.Subset == null)
{
return(table);
}
int nv = table.First().Key.Subset.LocalSubset.BitCount();
// Not worth reducing
if (table.Count * tr <= (1 << (nv - 1)))
{
return(table);
}
Dictionary <PartialSolution, int> result;
if (nv <= 1)
{
KeyValuePair <PartialSolution, int> minSol = table.Where((s) => s.Value == table.Values.Min()).First();
result = new Dictionary <PartialSolution, int>();
result.Add(minSol.Key, minSol.Value);
return(result);
}
RankBased irb = new RankBased(table.First().Key.Subset);
result = irb.M4RReduce(table);
RankBased.ClearPool();
return(result);
}
public Dictionary <PartialSolution, int> IntroduceEdgesIntoTable(Dictionary <PartialSolution, int> table, Edge[] edges)
{
if (table.Count == 0 || edges.Length == 0)
{
return(table);
}
Dictionary <PartialSolution, int> result = new Dictionary <PartialSolution, int>();
RankBased irb = new RankBased(table.First().Key.Subset);
PriorityQueue <PartialSolution> pq = new PriorityQueue <PartialSolution>(table.Count * 2);
foreach (KeyValuePair <PartialSolution, int> kvp in table)
{
pq.Enqueue(kvp.Key, kvp.Value);
}
HashSet <PartialSolution> seen = new HashSet <PartialSolution>();
while (!pq.IsEmpty())
{
int weight = (int)pq.PeekDist();
PartialSolution ps = pq.Dequeue();
// HashSet is faster than RankBased
if (!seen.Add(ps))
{
continue;
}
// Solution is already represented by output
if (!irb.AddSolution(ps))
{
continue;
}
result.Add(ps, weight);
Upsert(result, ps, weight);
// Add edges to ps. Note that adding edges is not necessary if solution is already represented (since we could have added the same edges to the representatives instead)
foreach (Edge e in edges)
{
if (ps.Find(e.To.Color) == ps.Find(e.From.Color))
{
continue;
}
PartialSolution newSol = new PartialSolution(ps.Subset, ps);
newSol.Union(e.To.Color, e.From.Color);
pq.Enqueue(newSol, weight + e.Weight);
}
}
RankBased.ClearPool();
return(result);
}
public Dictionary <int, Dictionary <PartialSolution, int> > Forget(TDNode bag, Vertex[] vertices, Dictionary <int, Dictionary <PartialSolution, int> > table)
{
forgetSW.Start();
Dictionary <int, Dictionary <PartialSolution, int> > result = new Dictionary <int, Dictionary <PartialSolution, int> >();
int vertexMask = 0;
foreach (Vertex v in vertices)
{
vertexMask |= (1 << v.Color);
}
byte[] tempUF = new byte[bag.ParentDecomposition.Width];
foreach (KeyValuePair <int, Dictionary <PartialSolution, int> > kvp in table)
{
int subset = kvp.Key;
int newSubset = subset & ~vertexMask;
Dictionary <PartialSolution, int> newDict = null;
if (!result.TryGetValue(newSubset, out newDict))
{
newDict = new Dictionary <PartialSolution, int>();
result.Add(newSubset, newDict);
}
foreach (KeyValuePair <PartialSolution, int> kvp2 in kvp.Value)
{
if (kvp2.Key.CountComponents() != kvp2.Key.CountComponents(newSubset))
{
continue; // Check whether set remains connected
}
VertexSubset newVertexSubset = VertexSubset.Create(bag, newSubset, kvp2.Key.Subset, null);
PartialSolution newPs = new PartialSolution(newVertexSubset, kvp2.Key);
Upsert(newDict, newPs, kvp2.Value);
}
}
foreach (KeyValuePair <int, Dictionary <PartialSolution, int> > kvp in table.ToList())
{
table[kvp.Key] = RankBased.Reduce(kvp.Value, 0.125);
}
forgetSW.Stop();
Program.TableCount += result.Values.Sum((t) => t.Count);
return(result);
}
// Joins two tables that have partial solutions with one type of vertex subset
public Dictionary <PartialSolution, int> JoinTwo(TDNode bag, List <int> verticesInvolved, Dictionary <PartialSolution, int> leftTable, Dictionary <PartialSolution, int> rightTable)
{
Dictionary <PartialSolution, int> newTable = new Dictionary <PartialSolution, int>();
// Reducing before Join is almost certainly beneficial, use a low threshold
leftTable = RankBased.Reduce(leftTable, 0.999);
rightTable = RankBased.Reduce(rightTable, 0.999);
KeyValuePair <PartialSolution, int>[] rightCopy = rightTable.ToArray();
foreach (KeyValuePair <PartialSolution, int> leftSol in leftTable)
{
foreach (KeyValuePair <PartialSolution, int> rightSol in rightCopy)
{
VertexSubset newSubset = VertexSubset.Create(bag, leftSol.Key.Subset.LocalSubset, leftSol.Key.Subset, rightSol.Key.Subset);
PartialSolution newSol = new PartialSolution(newSubset, leftSol.Key);
bool good = true;
foreach (int i in verticesInvolved)
{
byte rep = rightSol.Key.Find(i);
if (rep == i)
{
continue;
}
if (newSol.Find(i) == newSol.Find(rep))
{
good = false; break;
}
newSol.Union(i, rep);
}
if (good)
{
Upsert(newTable, newSol, leftSol.Value + rightSol.Value);
}
}
}
// Do not call reduce here: the forget, introduce or join bag that comes next will take care of it
//newTable = RankBased.Reduce(newTable, 0.5);
return(newTable);
}
public Dictionary <int, Dictionary <PartialSolution, int> > Introduce(TDNode bag, Vertex[] vertices, Dictionary <int, Dictionary <PartialSolution, int> > table)
{
introSW.Start();
Vertex[] terminals = vertices.Where((v) => v.IsTerminal).ToArray();
Vertex[] nonterminals = vertices.Where((v) => !v.IsTerminal).ToArray();
Dictionary <int, Dictionary <PartialSolution, int> > result = new Dictionary <int, Dictionary <PartialSolution, int> >();
for (int i = 0; i < (1 << nonterminals.Length); i++)
{
List <Vertex> toAdd = new List <Vertex>(terminals.Length + i.BitCount());
foreach (Vertex v in terminals)
{
toAdd.Add(v);
}
for (int j = 0; j < nonterminals.Length; j++)
{
if ((i & (1 << j)) != 0)
{
toAdd.Add(nonterminals[j]);
}
}
int addMask = 0;
foreach (Vertex v in toAdd)
{
addMask |= (1 << v.Color);
}
List <Edge> introEdges = new List <Edge>();
foreach (Vertex v in toAdd)
{
foreach (Edge e in v.Adj)
{
if (bag.Bag.Contains(e.To) && !introEdges.Contains(e))
{
introEdges.Add(e);
}
}
}
foreach (KeyValuePair <int, Dictionary <PartialSolution, int> > kvp in table)
{
int subset = kvp.Key;
int newSubset = subset | addMask;
Dictionary <PartialSolution, int> newDict = new Dictionary <PartialSolution, int>();
Dictionary <PartialSolution, int> localTable = RankBased.Reduce(kvp.Value, 0.999);
foreach (KeyValuePair <PartialSolution, int> kvp2 in localTable)
{
VertexSubset newVertexSubset = VertexSubset.Create(bag, newSubset, kvp2.Key.Subset, null);
newDict.Add(new PartialSolution(newVertexSubset, kvp2.Key), kvp2.Value);
}
if (introEdges.Where((e) => (newSubset & (1 << e.To.Color)) != 0).Count() > 2)
{
// Efficient method of introducing multiple edges at once and simultaneously running RankBased Reduce
//newDict = IntroduceEdgesIntoTable(newDict, introEdges.Where((e) => (newSubset & (1 << e.To.Color)) != 0).ToArray());
newDict = IntroduceEdgesIntoTable(newDict, introEdges.Where((e) => (newSubset & (1 << e.To.Color)) != 0).ToArray());
}
else
{
foreach (Edge e in introEdges)
{
if ((newSubset & (1 << e.To.Color)) != 0)
{
newDict = RankBased.Reduce(IntroduceEdge(newDict, e), 0.125);
}
}
}
if (newDict.Count > 0)
{
result.Add(newSubset, newDict);
}
}
}
introSW.Stop();
Program.TableCount += result.Values.Sum((t) => t.Count);
return(result);
}
// Different strategy for JoinTwo
// The column obtained by joining two partial solutions is the bitwise AND of the columns corresponding to both solutions
// Exploits this to attempt to speed up RBA
public Dictionary <PartialSolution, int> JoinTwoIncremental(TDNode bag, List <int> verticesInvolved, Dictionary <PartialSolution, int> leftTable, Dictionary <PartialSolution, int> rightTable)
{
Dictionary <PartialSolution, int> newTable = new Dictionary <PartialSolution, int>();
RankBased irbL = new RankBased(leftTable.First().Key.Subset);
RankBased irbR = new RankBased(rightTable.First().Key.Subset);
Tuple <KeyValuePair <PartialSolution, int>, Vector <uint>[]>[] leftSolutions = leftTable.OrderBy((kvp2) => kvp2.Value).Select((s) => Tuple.Create(s, irbL.GetColumn(s.Key))).ToArray();
Tuple <KeyValuePair <PartialSolution, int>, Vector <uint>[]>[] rightSolutions = rightTable.OrderBy((kvp2) => kvp2.Value).Select((s) => Tuple.Create(s, irbR.GetColumn(s.Key))).ToArray();
if (leftSolutions.Length > (1 << (verticesInvolved.Count - 1)))
{
for (int i = 0; i < leftSolutions.Length; i++)
{
if (!irbL.AddSolution(leftSolutions[i].Item1.Key, leftSolutions[i].Item2))
{
leftSolutions[i] = null;
}
}
}
if (rightSolutions.Length > (1 << (verticesInvolved.Count - 1)))
{
for (int i = 0; i < rightSolutions.Length; i++)
{
if (!irbR.AddSolution(rightSolutions[i].Item1.Key, rightSolutions[i].Item2))
{
rightSolutions[i] = null;
}
}
}
leftSolutions = leftSolutions.Where((s) => s != null).ToArray();
rightSolutions = rightSolutions.Where((s) => s != null).ToArray();
Tuple <PartialSolution, PartialSolution, Vector <uint>[], Vector <uint>[], int>[] joinedSolutions = new Tuple <PartialSolution, PartialSolution, Vector <uint>[], Vector <uint>[], int> [leftSolutions.Length * rightSolutions.Length];
int pos = 0;
foreach (Tuple <KeyValuePair <PartialSolution, int>, Vector <uint>[]> ls in leftSolutions)
{
foreach (Tuple <KeyValuePair <PartialSolution, int>, Vector <uint>[]> rs in rightSolutions)
{
joinedSolutions[pos++] = Tuple.Create(ls.Item1.Key, rs.Item1.Key, ls.Item2, rs.Item2, ls.Item1.Value + rs.Item1.Value);
}
}
joinedSolutions = joinedSolutions.OrderBy((s) => s.Item5).ToArray();
//leftTable = RankBasedReduce(leftTable, 1);
//rightTable = RankBasedReduce(rightTable, 1);
RankBased irbJoined = new RankBased(leftTable.First().Key.Subset);
HashSet <PartialSolution> psSeen = new HashSet <PartialSolution>();
foreach (Tuple <PartialSolution, PartialSolution, Vector <uint>[], Vector <uint>[], int> pair in joinedSolutions)
{
VertexSubset newSubset = VertexSubset.Create(bag, pair.Item1.Subset.LocalSubset, pair.Item1.Subset, pair.Item2.Subset);
PartialSolution newSol = new PartialSolution(newSubset, pair.Item1);
bool good = true;
foreach (int i in verticesInvolved)
{
byte rep = pair.Item2.Find(i);
if (rep == i)
{
continue;
}
if (newSol.Find(i) == newSol.Find(rep))
{
good = false; break;
}
newSol.Union(i, rep);
}
if (!good || !psSeen.Add(newSol))
{
continue;
}
Vector <uint>[] joinedColumn = RankBased.GetArray();
RankBased.AND(pair.Item3, pair.Item4, joinedColumn, irbJoined.rowCountVector);
if (!irbJoined.AddSolution(newSol, joinedColumn))
{
RankBased.ReleaseArray(joinedColumn);
continue;
}
newTable.Add(newSol, pair.Item5);
}
RankBased.ClearPool();
return(newTable);
}