IEnumerable <BitVector> enumerateCsgRecursive(JoinGraph graph, BitVector S, BitVector X)
{
// N = neighbour(S) \ X
BitVector N = SetOp.Substract(graph.NeighboursExcluding(S), X);
// Console.WriteLine("N: " + BitHelper.ToString(N));
// for all non-empty S' subsetof(N), emit (S union S')
if (N != SetOp.EmptySet)
{
VancePartition partitioner = new VancePartition(N);
foreach (var S_prime in partitioner.Next(true))
{
yield return(SetOp.Union(S, S_prime));
}
// for all non-empty S' subsetof(N), recursively invoke (graph, (S union S'), (X union N))
partitioner = new VancePartition(N);
foreach (var S_prime in partitioner.Next(true))
{
foreach (var v in enumerateCsgRecursive(graph,
SetOp.Union(S, S_prime), SetOp.Union(X, N)))
{
yield return(v);
}
}
}
}
// Naive partitioning
// Similar to DPBushy algorithm
IEnumerable <CsgCmpPair> NaiveNext(JoinGraph graph, BitVector S)
{
// it is connected because the 1st iteration is connected and when
// we generate for next iteration, we checked S1,S2.
//
Debug.Assert(graph.IsConnected(S));
VancePartition partitioner = new VancePartition(S);
foreach (var S1 in partitioner.Next())
{
c1_++;
BitVector S2 = SetOp.Substract(S, S1);
if (S1 < S2)
{
if (!graph.IsConnected(S1) || !graph.IsConnected(S2))
{
continue;
}
yield return(new CsgCmpPair(graph, S1, S2));
}
}
}
override internal PhysicNode Run(JoinGraph graph, BigInteger expectC1)
{
int ntables = graph.vertices_.Count;
Console.WriteLine("DP_Bushy #tables: " + ntables);
// initialization: enqueue all single tables
InitByInsertBasicTables(graph);
// loop through all candidates trees, CP included
ulong c1 = 0, c2 = 0;
for (BitVector S = 1; S < (1 << ntables); S++)
{
if (bestTree_[S] != null)
{
continue;
}
// need connected subgraphs if not consider CP
if (!graph.IsConnected(S))
{
// this partition enumeration is only to record #c2
c2 += (ulong)(new VancePartition(S)).Next().ToArray().Length;
continue;
}
// for all S_1 subset of S do
VancePartition partitioner = new VancePartition(S);
foreach (var S1 in partitioner.Next())
{
c2++;
BitVector S2 = SetOp.Substract(S, S1);
// requires S1 < S2 to avoid commutative duplication
Debug.Assert(S1 != S2);
if (S1 < S2)
{
// need connected subgraphs if not consider CP
if (!graph.IsConnected(S1) || !graph.IsConnected(S2))
{
continue;
}
// find a connected pair, get the best join tree between them
c1++;
var currTree = CreateMinimalJoinTree(bestTree_[S1], bestTree_[S2]);
Debug.Assert(bestTree_[S].Cost() == currTree.Cost());
}
}
}
// verify # loops for enumeration completeness:
// 1. mumber of bushy trees
// 2. expectC2/c2: number of trees DP considered (P68) and number of trees generated
// 3. expectC1/c1: number of trees considered
//
var nbushy = Space.Count_General_Bushy_CP(ntables);
var expectC2 = BigInteger.Pow(3, ntables) - BigInteger.Pow(2, ntables + 1) + 1;
Console.WriteLine("bushy: {0}, dp: {1} == c2: {2}; expected c1: {3} == c1: {4}",
nbushy, expectC2, c2,
expectC1, c1);
Debug.Assert(expectC2 == c2);
if (!expectC1.IsZero)
{
Debug.Assert(c1 == expectC1);
}
var result = bestTree_[(1 << ntables) - 1];
Console.WriteLine(result.Explain());
return(result);
}