public function createGraph()
{
$this->checkBalance();
// create resulting graph with supersource and supersink
$resultGraph = $this->graph->createGraphClone();
$superSource = $resultGraph->createVertex()->setLayoutAttribute('label', 's*');
$superSink = $resultGraph->createVertex()->setLayoutAttribute('label', 't*');
$sumBalance = 0;
// connect supersource s* and supersink t* with all "normal" sources and sinks
foreach ($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;
}
public function testNegativeComponents()
{
// 1 -- 2 3 --[-1]--> 4
// ^ |
// \---[-2]----/
$graph = new Graph();
$v1 = $graph->createVertex(1);
$v2 = $graph->createVertex(2);
$v3 = $graph->createVertex(3);
$v4 = $graph->createVertex(4);
$e1 = $v1->createEdge($v2);
$e2 = $v3->createEdgeTo($v4)->setWeight(-1);
$e3 = $v4->createEdgeTo($v3)->setWeight(-2);
$alg = new DetectNegativeCycle($graph);
$this->assertTrue($alg->hasCycleNegative());
$cycle = $alg->getCycleNegative();
$this->assertCount(2, $cycle->getEdges());
$this->assertCount(3, $cycle->getVertices());
$this->assertTrue($cycle->getVertices()->hasVertexId(3));
$this->assertTrue($cycle->getVertices()->hasVertexId(4));
}
