public PartialSolution(VertexSubset subset)
{
Subset = subset;
UnionFind = new byte[subset.ParentBag.ParentDecomposition.Width];
for (byte i = 0; i < UnionFind.Length; i++)
{
UnionFind[i] = i;
}
hashCode = 0;
}
public PartialSolution(int width)
{
Subset = null;
UnionFind = new byte[width];
for (byte i = 0; i < UnionFind.Length; i++)
{
UnionFind[i] = i;
}
hashCode = 0;
}
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);
}
public override bool Equals(object obj)
{
if (obj == null)
{
return(false);
}
VertexSubset objSet = obj as VertexSubset;
if (objSet == null)
{
return(false);
}
return(objSet.ParentBag == ParentBag && objSet.LocalSubset == LocalSubset && Object.ReferenceEquals(objSet.Left, Left) && Object.ReferenceEquals(objSet.Right, Right));
}
public static VertexSubset Create(TDNode ParentBag, int LocalSubset, VertexSubset Left, VertexSubset Right)
{
VertexSubset result = new VertexSubset()
{
ParentBag = ParentBag, LocalSubset = LocalSubset, Left = Left, Right = Right
};
return(result);
VertexSubset preExisting = null;
if (Lookup.TryGetValue(result, out preExisting))
{
return(preExisting);
}
Lookup[result] = result;
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> > Join(TDNode bag, Dictionary <int, Dictionary <PartialSolution, int> > left, Dictionary <int, Dictionary <PartialSolution, int> > right)
{
joinSW.Start();
Dictionary <int, Dictionary <PartialSolution, int> > result = new Dictionary <int, Dictionary <PartialSolution, int> >();
foreach (KeyValuePair <int, Dictionary <PartialSolution, int> > kvp in left)
{
Dictionary <PartialSolution, int> leftTable = kvp.Value;
Dictionary <PartialSolution, int> rightTable = null;
if (!right.TryGetValue(kvp.Key, out rightTable) || !leftTable.Any() || !rightTable.Any())
{
continue;
}
List <int> verticesInvolved = new List <int>();
foreach (Vertex v in bag.Bag)
{
if ((leftTable.First().Key.Subset.LocalSubset & (1 << v.Color)) != 0)
{
verticesInvolved.Add(v.Color);
}
}
Dictionary <PartialSolution, int> newTable;
newTable = JoinTwo(bag, verticesInvolved, leftTable, rightTable);
//newTable = JoinTwoIncremental(bag, verticesInvolved, leftTable, rightTable);
if (newTable.Count > 0)
{
result[kvp.Key] = newTable;
}
}
VertexSubset.ClearLookup();
joinSW.Stop();
Program.TableCount += result.Values.Sum((t) => t.Count);
return(result);
}
public T Compute <T>(IDPAlgorithm <T> algorithm, TDNode parent)
{
VertexSubset.ClearLookup();
// Note: through preprocessing, certain subtrees might have become empty. Do not consider.
IEnumerable <TDNode> children = Adj.Where((n) => n != parent && n.Subtree.Any());
if (children.Count() == 0)
{
return(algorithm.IntroduceEdges(algorithm.Introduce(this, Bag, algorithm.Leaf(ParentDecomposition.Width)), introduceEdges));
}
if (children.Count() == 1)
{
TDNode child = children.First();
Vertex[] toForget = child.Bag.Where((v) => !this.BagContains(v)).OrderBy((v) => v.Adj.Where((w) => BagContains(w.To)).Count()).Reverse().ToArray();
Vertex[] toIntroduce = this.Bag.Where((v) => !child.BagContains(v)).ToArray();
if (toIntroduce.Length > 0)
{
return(algorithm.IntroduceEdges(algorithm.Introduce(this, toIntroduce, child.Compute(algorithm, this)), introduceEdges));
}
if (toForget.Length > 0)
{
return(algorithm.IntroduceEdges(algorithm.Forget(this, toForget, child.Compute(algorithm, this)), introduceEdges));
}
// No change?
return(algorithm.IntroduceEdges(child.Compute(algorithm, this), introduceEdges));
}
if (children.Count() > 2)
{
throw new Exception("TD not preprocessed!");
}
TDNode left = children.ElementAt(0), right = children.ElementAt(1);
return(algorithm.IntroduceEdges(algorithm.Join(this, IntroduceIfNecessary(algorithm, left, left.Compute(algorithm, this)), IntroduceIfNecessary(algorithm, right, right.Compute(algorithm, this))), introduceEdges));
}
uint[] tempArray; // Temporary array used to generate column
public RankBased(VertexSubset subset)
{
vertices = new Vertex[subset.LocalSubset.BitCount()];
int pos = 0;
foreach (Vertex v in subset.ParentBag.Bag)
{
if ((subset.LocalSubset & (1 << v.Color)) != 0)
{
vertices[pos++] = v;
}
}
if (TW < vertices.Length - 1)
{
TW = vertices.Length - 1;
arrayPool.Clear();
inUsePool.Clear();
}
rowCount = 1 << (vertices.Length - 1);
if (rowCount < 1)
{
rowCount = 1;
}
rowCountVector = (rowCount + VectorLength - 1) / VectorLength;
elimOrder = new int[rowCount];
basisColumns = new Vector <uint> [rowCount][];
elimCount = 0;
orderEpos = new int[rowCount];
orderErem = new int[rowCount];
orderEmask = new uint[rowCount];
tempArray = new uint[rowCountVector * Vector <uint> .Count];
inputColumns = new Vector <uint> [rowCount][];
}
public PartialSolution(VertexSubset subset, PartialSolution parent)
{
Subset = subset;
UnionFind = new byte[subset == null ? 0 : subset.ParentBag.ParentDecomposition.Width];
for (byte i = 0; i < UnionFind.Length; i++)
{
UnionFind[i] = parent.UnionFind == null ? i : parent.UnionFind[i];
}
hashCode = 0;
// Check if any vertices have been forgotten
if (parent.Subset == null || ((subset.LocalSubset ^ parent.Subset.LocalSubset) & parent.Subset.LocalSubset) == 0)
{
return;
}
// Rework union-find to fix forgotten vertices
for (byte i = 0; i < UnionFind.Length; i++)
{
if ((Subset.LocalSubset & (1 << i)) != 0 && (parent.Subset.LocalSubset & (1 << i)) != 0)
{
byte rep = Find(i);
if ((Subset.LocalSubset & (1 << rep)) == 0)
{
UnionFind[rep] = i;
UnionFind[i] = i;
}
}
}
for (byte i = 0; i < UnionFind.Length; i++)
{
if ((Subset.LocalSubset & (1 << i)) == 0)
{
UnionFind[i] = i;
}
}
}
static void Main(string[] args)
{
int seed = 4321;
// Prescribed method of initializing randomness
if (Array.IndexOf(args, "-s") < args.Length - 1)
{
try
{
seed = int.Parse(args[Array.IndexOf(args, "-s") + 1]);
}
catch { }
}
Stopwatch sw = new Stopwatch();
//StreamWriter outSW = new StreamWriter("output.txt");
//Console.SetOut(outSW);
//for (int i = 79; i < 200; i += 2)
{
r = new Random(seed);
//outSW.Flush();
//if (i == 79) continue; // This testcase is very large and slow
sw.Restart();
//if (Debug) Console.Write(i.ToString().PadLeft(3, '0') + " ");
StreamReader sr = null;
//sr = new StreamReader(String.Format("../../../../../instances/instance{0}.gr", i.ToString().PadLeft(3, '0')));
g = Graph.Parse(sr ?? Console.In);
decomposition = TreeDecomposition.Parse(sr ?? Console.In, g);
InitUF(g);
List <Edge> forcedEdges = new List <Edge>();
// Find edges that are forced because they are between two terminals and there is no path with lighter bottleneck
foreach (Edge e in g.Edges.OrderBy((e) => e.Weight).ThenBy((e) => e.To.IsTerminal && e.From.IsTerminal ? 0 : 1))
{
if (Find(e.From.Id) == Find(e.To.Id))
{
continue;
}
if (e.To.IsTerminal && e.From.IsTerminal)
{
forcedEdges.Add(e);
}
Union(e.From.Id, e.To.Id);
}
if (Debug)
{
Console.WriteLine("Forced: " + forcedEdges.Count);
}
// Use Dreyfus-Wagner or Erickson-Monma-Veinott if FPT (in nubmer of terminals) is faster than treewidth DP
if (Math.Pow(5.0, decomposition.Width - Math.Log(1000000, 5.0)) > Math.Pow(3.0, g.Vertices.Where((v) => v.IsTerminal).Count() - forcedEdges.Count - Math.Log(1000000, 3.0)))
{
foreach (Edge e in forcedEdges)
{
if (e.From.IsTerminal)
{
e.From.IsTerminal = false;
}
else
{
e.To.IsTerminal = false;
}
e.From.Adj.Add(new Edge(e.From, e.To, 0));
e.To.Adj.Add(new Edge(e.To, e.From, 0));
}
//new DreyfusWagner(g, forcedEdges).Solve();
new EricksonMonmaVeinott(g, forcedEdges).Solve();
if (Debug)
{
Console.WriteLine(sw.ElapsedMilliseconds);
//continue; // Should be commented out when Debug is false
}
return;
}
XORCount = 0; TableCount = 0; GenerateCount = 0;
// Actually run the DP algorithm
decomposition.FindOptimalRoot();
SteinerAlgorithm algo = new SteinerAlgorithm();
Dictionary <int, Dictionary <PartialSolution, int> > result = decomposition.Compute(algo);
if (Debug)
{
algo.Diagnostics();
}
// Find best solution
int bestVal = int.MaxValue; PartialSolution bestSol = new PartialSolution();
foreach (Dictionary <PartialSolution, int> table in result.Values)
{
foreach (KeyValuePair <PartialSolution, int> kvp in table)
{
if (kvp.Value >= bestVal || kvp.Key.CountComponents() > 1)
{
continue;
}
bestVal = kvp.Value;
bestSol = kvp.Key;
}
}
if (bestVal == int.MaxValue)
{
Console.WriteLine("Impossible");
}
else
{
if (Debug)
{
Console.Write(Math.Round(sw.ElapsedMilliseconds / 1000.0, 1) + "s\tSolutions: {0}\tRows Generated: {1}\tXORCount: {2}\t", TableCount, GenerateCount, XORCount);
}
Console.WriteLine("VALUE " + bestVal);
if (Debug)
{
Console.WriteLine();
}
// Reconstruct subset of vertices
HashSet <int> solution = new HashSet <int>();
Stack <VertexSubset> subsets = new Stack <VertexSubset>();
subsets.Push(bestSol.Subset);
while (subsets.Count > 0)
{
VertexSubset subset = subsets.Pop();
if (subset == null || subset.ParentBag == null)
{
continue;
}
subsets.Push(subset.Left); subsets.Push(subset.Right);
foreach (Vertex v in subset.ParentBag.Bag)
{
if ((subset.LocalSubset & (1 << v.Color)) != 0)
{
solution.Add(v.Id);
}
}
}
InitUF(g);
// Compute MST on vertex set
int total = 0; int count = 0;
foreach (Edge e in g.Edges.OrderBy((e) => e.Weight).ThenBy((e) => Math.Min(e.To.Id, e.From.Id)).ThenBy((e) => Math.Max(e.To.Id, e.From.Id)))
{
if (!solution.Contains(e.To.Id) || !solution.Contains(e.From.Id))
{
continue;
}
if (Find(e.To.Id) == Find(e.From.Id))
{
continue;
}
Union(e.To.Id, e.From.Id);
if (!Debug)
{
Console.WriteLine(Math.Min((e.From.Id + 1), (e.To.Id + 1)) + " " + Math.Max((e.From.Id + 1), (e.To.Id + 1)));
}
total += e.Weight;
count++;
}
}
}
if (Debug)
{
Console.ReadLine();
}
}
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);
}