public static Point2 LiftSigmaD(Point2 startPoint)
{
int[] intArray = new int[startPoint.GetDimension()];
int sigma_dMinus1 = (int)Math.Pow(2, startPoint.GetDimension() - 1);
for (int i = 0; i < intArray.Length; i++)
{
intArray[i] = sigma_dMinus1 - startPoint.Coordinates[i];
}
Point2 temp = new Point2(intArray);
temp.IncreaseDimensionality(0, 0);
return(temp);
}
//returns true if candidate vertex can be decomposed in multiple ways from set of possible edges.
private bool DoubleDecompositionHeuristic(Point2 candidateVertex, List <Point2> possibleEdges)
{
return(DoubleDecompositionBruteForce(candidateVertex, possibleEdges));
//possibleEdges may not be required.
var numberOfNonZeroCoordinates = candidateVertex.GetDimension();
List <Point2> usedVectors = new List <Point2>();
//create data structure to store (2) decompositions of candidate vertices.
//make a copy of candidateVertex that will be modified (i.e. subtracting vectors).
while (true) //need to determine termination condition for loop
{
//find first nonzero coordinate of current vector
var firstNonZeroIndex = candidateVertex.FirstNonZeroIndex();
List <Point2> splitVectors = new List <Point2>();
//generate corresponding unit vector
Point2 unitVector = Point2.GenerateOnesVector(candidateVertex.GetDimension(), firstNonZeroIndex);
//ensure unit vector is not in usedVector list, if vector is used, perform split. Check to make sure split vectors are not used before.
if (usedVectors.Contains(unitVector))
{
splitVectors = Point2.SplitVectors(unitVector, usedVectors);
}
if (splitVectors.Count == 0)
{
//Cannot split the current vector, hence no decomposition possible
}
//subtract unit vector from current vector
//add unit vector to usedVeectorList
}
return(DoubleDecompositionBruteForce(candidateVertex, possibleEdges));
}
public static List <Point2> GenerateV(Point2 u)
{
var result = new List <Point2>();
var candidateV = new Point2();
var vCoordinates = new int[u.GetDimension()];
var g0 = new int[Globals.d];
var terminateFlag = false;
//set first v candidate
for (int i = 0; i < u.GetDimension(); i++)
{
vCoordinates[i] = Globals.k - u.Coordinates[i] - Globals.gap;
}
while (!terminateFlag)
{
candidateV = new Point2(vCoordinates);
//same point check
if (u.Equals(candidateV))
{
if (Globals.ShowMessages)
{
Console.WriteLine(candidateV.ToString() + ": Eliminated. Same point as u.");
}
}
//inverse check
else if (CheckInverse(u, candidateV))
{
if (Globals.ShowMessages)
{
Console.WriteLine(candidateV.ToString() + ": Eliminated. Inverse already checked.");
}
}
else
{
var uRedundant = false;
var vRedundant = false;
//generate gi
for (int i = 0; i < Globals.d; i++)
{
g0[i] = Globals.gap + u.Coordinates[i] + vCoordinates[i] - Globals.k;
}
//check vStar, given gap i, check that both u and v exist within the vertex set of the corresponding facets.
if (!CheckVertexSet(u, candidateV, g0, Globals.d - 1, Globals.k))
{
if (Globals.ShowMessages)
{
Console.WriteLine(candidateV.ToString() + ": Eliminated. Point does not belong to vertex set.");
}
}
//check convex core
else if (CheckConvexCore(u, candidateV, g0, out uRedundant, out vRedundant))
{
result.Add(candidateV);
if (Globals.ShowMessages)
{
Console.WriteLine("u: " + u + ". v: " + candidateV);
}
}
else
{
if (Globals.ShowMessages)
{
Console.Write("u: " + u + ". v: ");
foreach (int i in vCoordinates)
{
Console.Write(i + " ");
}
Console.WriteLine(" eliminated, " + (uRedundant && vRedundant ? "u and v are not vertices " :
(uRedundant ? "u is not a vertex " : "v is not a vertex ")) +
"of the convex core.");
}
}
result.Add(candidateV);
if (Globals.ShowMessages)
{
Console.WriteLine("u: " + u + ". v: " + candidateV);
}
}
//increment candidate and check termination condition
while (symmetryCheck(u.Coordinates, vCoordinates))
{
IncrementCandidatePoint(u.Coordinates, vCoordinates, out terminateFlag);
}
}
return(result);
}
