public Formula ReduceVertexCoverToSat(AdjacentMap pUndirectedGraph, int pMinVertexCount)
{
Dictionary <string, Variable> variables = new Dictionary <string, Variable>();
foreach (var key in pUndirectedGraph.Keys)
{
for (int i = 1; i <= pMinVertexCount; i++)
{
variables.Add($"{key}|{i}", new Variable($"{key}|{i}"));
}
}
Console.WriteLine("Created Variables");
foreach (var variable in variables)
{
Console.WriteLine(variable.Value.ToString());
}
var formula = new Formula();
for (int i = 1; i <= pMinVertexCount; i++)
{
if (i > 1)
{
formula.Add(_and);
}
var atMostOneList = variables.Values.Where(v => v.Name.EndsWith($"|{i}")).ToList();
var atMostOneFormular = AtMostOne(atMostOneList);
formula.AddRange(atMostOneFormular);
}
List <string> processedEdges = new List <string>();
foreach (var key in pUndirectedGraph.Keys)
{
foreach (var adjacent in pUndirectedGraph[key])
{
if (!processedEdges.Contains($"{key}|{adjacent}") && !processedEdges.Contains($"{adjacent}|{key}"))
{
var atLeastOneList = new List <Variable>();
for (int i = 1; i <= pMinVertexCount; i++)
{
atLeastOneList.Add(variables[$"{key}|{i}"]);
atLeastOneList.Add(variables[$"{adjacent}|{i}"]);
}
var atleastOneFormular = AtLeastOne(atLeastOneList);
formula.Add(_and);
formula.Add(atleastOneFormular);
processedEdges.Add($"{key}|{adjacent}");
}
}
}
return(formula);
}
