public function getEdges()
{
$alg = new Directed($this->graph);
if ($alg->hasDirected()) {
throw new UnexpectedValueException('Input graph contains directed edges');
}
$alg = new Groups($this->graph);
if (!$alg->isBipartit()) {
throw new UnexpectedValueException('Input graph does not have bipartit groups assigned to each vertex. Consider Using "AlgorithmBipartit::createGraph()" first');
}
// create temporary flow graph with supersource and supersink
$graphFlow = $this->graph->createGraphCloneEdgeless();
$superSource = $graphFlow->createVertex();
$superSink = $graphFlow->createVertex();
$groups = $alg->getGroups();
$groupA = $groups[0];
$groupB = $groups[1];
// connect supersource s* to set A and supersink t* to set B
foreach ($graphFlow->getVertices() as $vertex) {
// we want to skip over supersource & supersink as they do not have a partition assigned
if ($vertex === $superSource || $vertex === $superSink) {
continue;
}
$group = $vertex->getGroup();
// source
if ($group === $groupA) {
$superSource->createEdgeTo($vertex)->setCapacity(1)->setFlow(0);
// temporarily create edges from A->B for flow graph
$originalVertex = $this->graph->getVertex($vertex->getId());
foreach ($originalVertex->getVerticesEdgeTo() as $vertexTarget) {
$vertex->createEdgeTo($graphFlow->getVertex($vertexTarget->getId()))->setCapacity(1)->setFlow(0);
}
// sink
} elseif ($group === $groupB) {
$vertex->createEdgeTo($superSink)->setCapacity(1)->setFlow(0);
} else {
// @codeCoverageIgnoreStart
throw new LogicException('Should not happen. Unknown set: ' + $belongingSet);
// @codeCoverageIgnoreEnd
}
}
// visualize($resultGraph);
// calculate (s*, t*)-flow
$algMaxFlow = new MaxFlowEdmondsKarp($superSource, $superSink);
$resultGraph = $algMaxFlow->createGraph();
// destroy temporary supersource and supersink again
$resultGraph->getVertex($superSink->getId())->destroy();
$resultGraph->getVertex($superSource->getId())->destroy();
$returnEdges = array();
foreach ($resultGraph->getEdges() as $edge) {
// only keep matched edges
if ($edge->getFlow() > 0) {
$originalEdge = $this->graph->getEdgeClone($edge);
$returnEdges[] = $originalEdge;
}
}
return new Edges($returnEdges);
}
public function createGraph()
{
$this->checkBalance();
// create resulting graph with supersource and supersink
$resultGraph = $this->graph->createGraphClone();
$superSource = $resultGraph->createVertex();
$superSink = $resultGraph->createVertex();
$sumBalance = 0;
// connect supersource s* and supersink t* with all "normal" sources and sinks
foreach ($resultGraph->getVertices() as $vertex) {
$balance = $vertex->getBalance();
if ($balance > 0) {
// positive balance => source capacity
$superSource->createEdgeTo($vertex)->setCapacity($balance);
$sumBalance += $balance;
} elseif ($balance < 0) {
// negative balance => sink capacity (positive)
$vertex->createEdgeTo($superSink)->setCapacity(-$balance);
}
}
// calculate (s*, t*)-flow
$algMaxFlow = new MaxFlowEdmondsKarp($superSource, $superSink);
$flowMax = $algMaxFlow->getFlowMax();
if ($flowMax !== $sumBalance) {
throw new UnexpectedValueException('Network does not support required flow of ' . $sumBalance . ' (maximum possible flow limited to ' . $flowMax . ')');
}
$resultGraph = $algMaxFlow->createGraph();
while (true) {
// create residual graph
$algRG = new ResidualGraph($resultGraph);
$residualGraph = $algRG->createGraph();
// get negative cycle
$alg = new DetectNegativeCycle($residualGraph);
try {
$clonedEdges = $alg->getCycleNegative()->getEdges();
} catch (UnderflowException $ignore) {
// no negative cycle found => end algorithm
break;
}
// calculate maximal possible flow = minimum capacity remaining for all edges
$newFlow = $clonedEdges->getEdgeOrder(Edges::ORDER_CAPACITY_REMAINING)->getCapacityRemaining();
// set flow on original graph
$this->addFlow($resultGraph, $clonedEdges, $newFlow);
}
// destroy temporary supersource and supersink again
$resultGraph->getVertex($superSink->getId())->destroy();
$resultGraph->getVertex($superSource->getId())->destroy();
return $resultGraph;
}