} // GetNodeToDrop
static List <int> MakeOneMissing(MaxCliqueGraph graph, List <int> clique)
{
int count;
List <int> result = new List <int>();
for (int i = 0; i < graph.NumberNodes; ++i)
{
if (graph.NumberNeighbors(i) < clique.Count - 1)
{
continue;
}
if (clique.BinarySearch(i) >= 0)
{
continue;
}
count = 0;
for (int j = 0; j < clique.Count; ++j)
{
if (graph.AreAdjacent(i, clique[j]))
{
++count;
}
}
if (count == clique.Count - 1)
{
result.Add(i);
}
}
return(result);
}
static bool FormsALargerClique(MaxCliqueGraph graph, List <int> clique, int node)
{
for (int i = 0; i < clique.Count; ++i)
{
if (graph.AreAdjacent(clique[i], node) == false)
{
return(false);
}
}
return(true);
}
static List <int> MakePossibleAdd(MaxCliqueGraph graph, List <int> clique)
{
List <int> result = new List <int>();
for (int i = 0; i < graph.NumberNodes; ++i)
{
if (FormsALargerClique(graph, clique, i) == true)
{
result.Add(i);
}
}
return(result);
}
static int UpdateProhibitPeriod(MaxCliqueGraph graph, List <int> clique,
int bestSize, Dictionary <int, CliqueInfo> history, int time, int prohibitPeriod,
ref int timeProhibitChanged)
{
int result = prohibitPeriod;
CliqueInfo cliqueInfo = new CliqueInfo(clique, time);
if (history.ContainsKey(cliqueInfo.GetHashCode()))
{
CliqueInfo ci = history[cliqueInfo.GetHashCode()];
int intervalSinceLastVisit = time - ci.LastSeen;
ci.LastSeen = time;
if (intervalSinceLastVisit < 2 * graph.NumberNodes - 1)
{
timeProhibitChanged = time;
if (prohibitPeriod + 1 < 2 * bestSize)
{
return(prohibitPeriod + 1);
}
else
{
return(2 * bestSize);
}
}
}
else
{
history.Add(cliqueInfo.GetHashCode(), cliqueInfo);
}
if (time - timeProhibitChanged > 10 * bestSize)
{
timeProhibitChanged = time;
if (prohibitPeriod - 1 > 1)
{
return(prohibitPeriod - 1);
}
else
{
return(1);
}
}
else
{
return(result); // нет изменений
}
} // UpdateProhibitTime
static int GetNodeToDrop(MaxCliqueGraph graph, List <int> clique, List <int> oneMissing)
{
if (clique.Count == 1)
{
return(clique[0]);
}
List <int> cliqueCountNotAdjacent = new List <int>(clique.Count);
int maxCount = 0;
for (int i = 0; i < clique.Count; ++i)
{
int currCliqueNode = clique[i];
int countNotAdjacent = 0;
for (int j = 0; j < oneMissing.Count; ++j)
{
int currOneMissingNode = oneMissing[j];
if (graph.AreAdjacent(currCliqueNode,
currOneMissingNode) == false)
{
++countNotAdjacent;
}
}
cliqueCountNotAdjacent.Add(countNotAdjacent);
if (countNotAdjacent > maxCount)
{
maxCount = countNotAdjacent;
}
}
List <int> candidates = new List <int>();
for (int i = 0; i < clique.Count; ++i)
{
if (cliqueCountNotAdjacent[i] == maxCount)
{
candidates.Add(clique[i]);
}
}
if (candidates.Count == 1)
{
return(candidates[0]);
}
return(candidates[random.Next(0, candidates.Count)]);
} // GetNodeToDrop
static int GetNodeToAdd(MaxCliqueGraph graph, List <int> allowedAdd, List <int> possibleAdd)
{
if (allowedAdd.Count == 1)
{
return(allowedAdd[0]);
}
List <int> allowedAddDegree = new List <int>(possibleAdd.Count);
int maxDegree = 0;
for (int i = 0; i < allowedAdd.Count; ++i)
{
int currNode = allowedAdd[i];
int degreeOfCurrentNode = 0;
for (int j = 0; j < possibleAdd.Count; ++j)
{
int otherNode = possibleAdd[j];
if (graph.AreAdjacent(currNode, otherNode) == true)
{
++degreeOfCurrentNode;
}
}
allowedAddDegree.Add(degreeOfCurrentNode);
if (degreeOfCurrentNode > maxDegree)
{
maxDegree = degreeOfCurrentNode;
}
}
List <int> candidates = new List <int>();
for (int i = 0; i < allowedAdd.Count; ++i)
{
if (allowedAddDegree[i] == maxDegree)
{
candidates.Add(possibleAdd[i]);
}
}
if (candidates.Count == 1)
{
return(candidates[0]);
}
return(candidates[random.Next(0, candidates.Count)]);
}
static void Main(string[] args)
{
try
{
Console.WriteLine("\nBegin greedy maximum clique demo\n");
Console.WriteLine("\nBegin tabu algorithm maximum clique demo\n");
string graphFile = "..\\..\\DimacsGraph.clq"; //string graphFile = "DimacsGraph.clq";
MaxCliqueGraph.ValidateGraphFile(graphFile, FileFormat.DIMACS); //"DIMACS"
MaxCliqueGraph graph = new MaxCliqueGraph(graphFile, FileFormat.DIMACS);
graph.ValidateGraph();
Console.WriteLine("Loading graph into memory");
Console.WriteLine("Graph loaded and validated\n");
int maxTime = 50; // В настоящей задаче о максимальной клике maxTime обычно находится в диапазоне от 1000 до 100 000.
int targetCliqueSize = graph.NumberNodes;
List <int> maxClique = FindMaxClique(graph, maxTime, targetCliqueSize);
Console.WriteLine("\nMaximum time reached");
Console.WriteLine("\nSize of best clique found = " + maxClique.Count);
Console.WriteLine("\nBest clique found:");
Console.WriteLine(ListAsString(maxClique));
Console.WriteLine("\nEnd greedy maximum clique demo\n");
Console.WriteLine(graph.ToString());
Console.WriteLine("\nAre nodes 5 and 8 adjacent? " +
graph.AreAdjacent(5, 8));
Console.WriteLine("Number neighbors of node 4 = " +
graph.NumberNeighbors(4));
WriteFile(ListAsString(maxClique), "output.txt");
string outputGraphFile = "..\\..\\output.txt";
graph.SaveTxtFormatGraph(outputGraphFile);
}
catch (Exception ex)
{
Console.WriteLine("Fatal: " + ex.Message);
}
} // Main
static List <int> FindMaxClique(MaxCliqueGraph graph, int maxTime, int targetCliqueSize)
{
List <int> clique = new List <int>();
random = new Random(1);
int time = 0;
int timeBestCliqueFound = 0; //timeBestClique
int timeLastRestart = 0; //timeRestart
int nodeToAdd = -1;
int nodeToDrop = -1;
int prohibitPeriod = 1;
int timeProhibitChanged = 0;
int[] lastMoved = new int[graph.NumberNodes];
for (int i = 0; i < lastMoved.Length; ++i)
{
lastMoved[i] = int.MinValue;
}
Dictionary <int, CliqueInfo> history = new Dictionary <int, CliqueInfo>();
int randomNode = random.Next(0, graph.NumberNodes);
Console.WriteLine("Adding node " + randomNode);
clique.Add(randomNode);
List <int> bestClique = new List <int>();
bestClique.AddRange(clique);
int bestSize = bestClique.Count;
timeBestCliqueFound = time;
//int timeBestCliqueFound = 0;
//int timeLastRestart = 0;
List <int> possibleAdd = MakePossibleAdd(graph, clique);
List <int> oneMissing = MakeOneMissing(graph, clique);
while (time < maxTime && bestSize < targetCliqueSize)
{
++time;
bool cliqueChanged = false;
ValidateClique(clique, possibleAdd, oneMissing);
if (possibleAdd.Count > 0)
{
List <int> allowedAdd = SelectAllowedNodes(possibleAdd, time, prohibitPeriod, lastMoved);
if (allowedAdd.Count > 0)
{
nodeToAdd = GetNodeToAdd(graph, allowedAdd, possibleAdd);
Console.WriteLine("Adding node " + nodeToAdd);
clique.Add(nodeToAdd);
lastMoved[nodeToAdd] = time;
clique.Sort();
cliqueChanged = true;
if (clique.Count > bestSize)
{
bestSize = clique.Count;
bestClique.Clear();
bestClique.AddRange(clique);
timeBestCliqueFound = time;
}
}
} // добавление
if (cliqueChanged == false)
{
if (clique.Count > 0)
{
List <int> allowedInClique = SelectAllowedNodes(clique, time, prohibitPeriod, lastMoved);
if (allowedInClique.Count > 0)
{
nodeToDrop = GetNodeToDrop(graph, clique, oneMissing);
Console.WriteLine("Dropping node " + nodeToDrop);
clique.Remove(nodeToDrop);
lastMoved[nodeToDrop] = time;
clique.Sort();
cliqueChanged = true;
}
}
} // удаление
if (cliqueChanged == false) // если невозможно добавить или удалить разрешенный узел
{
if (clique.Count > 0)
{
nodeToDrop = clique[random.Next(0, clique.Count)];
clique.Remove(nodeToDrop);
lastMoved[nodeToDrop] = time;
clique.Sort();
cliqueChanged = true;
}
}
int restart = 2 * bestSize; // 100
if (time - timeBestCliqueFound > restart &&
time - timeLastRestart > restart)
{
Console.WriteLine("\nRestarting\n");
timeLastRestart = time;
prohibitPeriod = 1;
timeProhibitChanged = time;
history.Clear();
int seedNode = -1;
List <int> temp = new List <int>();
for (int i = 0; i < lastMoved.Length; ++i)
{
if (lastMoved[i] == int.MinValue)
{
temp.Add(i);
}
}
if (temp.Count > 0)
{
seedNode = temp[random.Next(0, temp.Count)];
}
else
{
seedNode = random.Next(0, graph.NumberNodes);
}
clique.Clear();
clique.Add(seedNode);
Console.WriteLine("Adding node " + seedNode);
} // перезапуск
possibleAdd = MakePossibleAdd(graph, clique); // Альтернатива — поддерживать вспомогательные структуры данных
oneMissing = MakeOneMissing(graph, clique); // и обновлять эти два списка вместо повторного их создания с нуля.
prohibitPeriod = UpdateProhibitPeriod(graph, clique, bestSize,
history, time, prohibitPeriod, ref timeProhibitChanged);
} // основной цикл обработки
return(bestClique);
}