//---------------------------------------------------------
//actual call
//minDegree default 2, all other nodes are skipped
//only high values have an impact because we only
//work on triconnected components, skipping all low
//degree nodes (but we make the test graphcopy biconnected
//afterwards)
void CliqueFinder::doCall(int minDegree)
{
//---------------------------------------------
//initialize structures and check preconditions
//---------------------------------------------
m_copyCliqueNumber.init(*m_pCopy, -1);
m_usedNode.init(*m_pCopy, false);
makeParallelFreeUndirected(*m_pCopy); //it doesnt make sense to count loops
makeLoopFree(*m_pCopy); //or parallel edges
m_numberOfCliques = 0;
//We first indentify the biconnected components of
//the graph to allow the use of the SPQR-tree data
//Structure. Latter then separates the different
//triconnected components on which we finally work
//TODO: delete all copy nodes with degree < minDegree
int nodeNum = m_pGraph->numberOfNodes();
//TODO: change for non-cliques, where this is not necessary
if (nodeNum < minDegree) return; //nothing to find for cliques
//-------------------------------------------------------
//Special cases:
//Precondition for SPQR-trees: graph has at least 3 nodes
//or 2 nodes and at least 3 edges
//TODO: check this after makebiconnected
//----------------------------
//set values for trivial cases
if (nodeNum < 3)
{
//only set numbers for the special case
if (nodeNum == 2)
{
if (m_pGraph->numberOfEdges() >= 1) //> 2)
{
node w = m_pCopy->firstNode();
m_copyCliqueNumber[w] = 0;
w = w->succ();
m_copyCliqueNumber[w] = 0;
}
else
{
if (minDegree == 0)
{
node w = m_pCopy->firstNode();
m_copyCliqueNumber[w] = 0;
w = w->succ();
m_copyCliqueNumber[w] = 1;
}//if no mindegree
}
}//if two nodes
else if ( (nodeNum == 1) && (minDegree <= 0))
m_copyCliqueNumber[m_pCopy->firstNode()] = 0;
return;
}//graph too small
OGDF_ASSERT(m_pCopy != 0)
//save the original edges
EdgeArray<bool> originalEdge(*m_pCopy, true);
List<edge> added;
//we make the copy biconnected, this keeps the triconnected
//components
//-------------------------------------------------------------
//store the original node degrees:
//afterwards we want to be able to sort the nodes corresponding
//to their real degree, not the one with the additional
//connectivity edges
NodeArray<int> realDegree(*m_pCopy, -1);//no isolated nodes exist here
//relative degree, number of high degree neighbours
NodeArray<int> relDegree(*m_pCopy, 0);//no isolated nodes exist here
for(node v : m_pCopy->nodes)
{
realDegree[v] = v->degree();
if (v->degree() > 0)
{
adjEntry adRun = v->firstAdj();
while (adRun)
{
adjEntry succ = adRun->succ();
if (adRun->twinNode()->degree() >= minDegree)
relDegree[v]++;
adRun = succ;
}//while
}//if not isolated
}
makeBiconnected(*m_pCopy, added);
//TODO: We can decrease node degrees by the number of adjacent
//low degree nodes to sort them only by number of relevant connections
//PARTIALLY DONE: relDegree
//storing the component number, there are no isolated nodes now
EdgeArray<int> component(*m_pCopy);
StaticSPQRTree spqrTree(*m_pCopy);
//Return if there are no R-nodes
if (spqrTree.numberOfRNodes() == 0)
{
//TODO:set node numbers for cliques
//that are not triconnected
//each edge is a min. clique for mindegree 1
//each triangle for mindegree 2?
return;
}//if
//the degree of the original node
//within the triconnected component
NodeArray<int> ccDegree(*m_pCopy, 0);
for(node v : spqrTree.tree().nodes)
{
//we search for dense subgraphs in R-Nodes
//heuristics:
//sort the nodes by their degree within the component
//in descending order, then start cliques by initializing
//them with the first node and checking the remaining,
//starting new cliques with nodes that don't fit in the
//existing cliques (stored in cliqueList)
if (spqrTree.typeOf(v) == SPQRTree::RNode)
{
//retrieve the skeleton
Skeleton &s = spqrTree.skeleton(v);
Graph &skeletonG = s.getGraph();
//list of cliques
List< List<node>* > cliqueList;
//we insert all nodes into a list to sort them
List<node> sortList;
//save the usable edges within the triconnected component
EdgeArray<bool> usableEdge(*m_pCopy, false);
//derive the degree of the original node
//within the triconnected component
for(node w : skeletonG.nodes)
{
node vOrig = s.original(w);
edge eSkel;
forall_adj_edges(eSkel, w)
{
edge goodEdge = s.realEdge(eSkel);
bool isGoodEdge = goodEdge != nullptr;
if (isGoodEdge) isGoodEdge = m_pCopy->original(goodEdge) != nullptr;
//if (s.realEdge(eSkel))
if (isGoodEdge)
{
ccDegree[vOrig]++;
usableEdge[goodEdge] = true;
}
}//foralladjedges
sortList.pushBack(vOrig);
}
//sort the nodes corresponding to their degree
NodeComparer<int> ncomp(ccDegree, false);
sortList.quicksort(ncomp);
ListIterator<node> itNode = sortList.begin();
while(itNode.valid())
{
//hier erst vergleichen, ob Knoten Grad > aktcliquengroesse,
//dann ob mit clique verbunden
//alternativ koennte man stattdessen fuer jeden gewaehlten
//Knoten nur noch seine Nachbarn als Kandidaten zulassen
//hier sollte man mal ein paar Strategien testen, z.B.
//streng nach Listenordnung vorgehen oder eine "Breitensuche"
//vom Startknoten aus..
node vCand = *itNode;
//node can appear in several 3connected components
if (m_usedNode[vCand])
{
++itNode;
continue;
}//if already used
//if there are only "small" degree nodes left, we stop
//if (vCand->degree() < minDegree)
if (ccDegree[vCand] < minDegree)
break;
//------------------------------------------------
//successively check the node against the existing
//clique candidates
//run through the clique candidates to find a matching
//node set
bool setFound = false;
ListIterator< List<node>* > itCand = cliqueList.begin();
while (itCand.valid())
{
//in the case of cliques, the node needs min degree
//greater or equal to current clique size
//TODO: adapt to dense subgraphs
bool isCand = false;
if (m_density == 100)
isCand = (vCand->degree() >= (*itCand)->size());
else isCand = (vCand->degree() >= ceil(m_density*(*itCand)->size()/100.0));
if (isCand)
{
//TODO: insert adjacency oracle here to speed
//up the check?
//TODO: check if change from clique to dense subgraph criterion
//violates some preconditions for our search
if (allAdjacent(vCand, (*itCand)))
{
OGDF_ASSERT(m_usedNode[*itNode] == false)
(*itCand)->pushBack(*itNode);
setFound = true;
m_usedNode[(*itNode)] = true;
//bubble sort the clique after insertion of the node
//while size > predsize swap positions
ListIterator< List<node>* > itSearch = itCand.pred();
if (itSearch.valid())
{
while (itSearch.valid() &&
( (*itCand)->size() > (*itSearch)->size()) )
{
--itSearch;
}
//If valid, move behind itSearch, else move to front
if (!itSearch.valid())
cliqueList.moveToFront(itCand);
else cliqueList.moveToSucc(itCand, itSearch);
}//if valid
break;
}//if node fits into node set
}//if sufficient degree
//hier kann man mit else breaken, wenn Liste immer sortiert ist
++itCand;
}//while clique candidates
//create a new candidate if necessary
if (!setFound)
{
List<node>* cliqueCandidate = OGDF_NEW List<node>();
itCand = cliqueList.pushBack(cliqueCandidate);
OGDF_ASSERT(m_usedNode[*itNode] == false)
cliqueCandidate->pushBack(*itNode);
m_usedNode[(*itNode)] = true;
}//if no candidate yet
++itNode;
}//while valid
//TODO: cliquelist vielleicht durch einen member ersetzen
//und nicht das delete vergessen!
#ifdef OGDF_DEBUG
//int numC1 = cliqueList.size();
//int nodeNum = 0;
//for (List<node> *pL : cliqueList)
//{
// if ( pL->size() > minDegree )
// nodeNum = nodeNum + pL->size();
//}
checkCliques(cliqueList, false);
//double realTime;
//ogdf::usedTime(realTime);
#endif
postProcessCliques(cliqueList, usableEdge);
#ifdef OGDF_DEBUG
//realTime = ogdf::usedTime(realTime);
//int nodeNum2 = 0;
//for (List<node> *pL : cliqueList)
//{
// if ( pL->size() > minDegree )
// nodeNum2 = nodeNum2 + pL->size();
//}
//if (nodeNum2 > nodeNum)
//{
// cout<<"\nAnzahl Cliquen vor PP: "<<numC1<<"\n";
// cout<<"Anzahl Cliquen nach PP: "<<cliqueList.size()<<"\n";
// cout<<"Anzahl Knoten in grossen Cliquen: "<<nodeNum<<"\n";
// cout<<"Anzahl Knoten danach in grossen Cliquen: "<<nodeNum2<<"\n\n";
//}
//cout << "Used postprocessing time: " << realTime << "\n" << flush;
checkCliques(cliqueList, false);
#endif
//now we run through the list until the remaining node sets
//are to small to be of interest
for(List<node> *pCand : cliqueList)
{
if ( pCand->size() <= minDegree ) break;
for(node u : *pCand)
{
OGDF_ASSERT(m_copyCliqueNumber[u] == -1)
m_copyCliqueNumber[u] = m_numberOfCliques;
}//for clique nodes
m_numberOfCliques++;
}
//TODO: only set numbers if return value is not a list
//of clique node lists
setResults(cliqueList);
//free the allocated memory
for(List<node> *pCl : cliqueList)
{
delete pCl;
}
}//if
void DfsMakeBiconnected::doCall(Graph &G, List<edge> &L)
{
makeBiconnected(G,L);
}