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;
}
/**
* Returns max flow graph
*
* @return Graph
*/
public function createGraph()
{
$graphResult = $this->startVertex->getGraph()->createGraphClone();
// initialize null flow and check edges
foreach ($graphResult->getEdges() as $edge) {
if (!$edge instanceof EdgeDirected) {
throw new UnexpectedValueException('Undirected edges not supported for edmonds karp');
}
$edge->setFlow(0);
}
$idA = $this->startVertex->getId();
$idB = $this->destinationVertex->getId();
do {
// Generate new residual graph and repeat
$residualAlgorithm = new ResidualGraph($graphResult);
$graphResidual = $residualAlgorithm->createGraph();
// 1. Search _shortest_ (number of hops and cheapest) path from s -> t
$alg = new BreadthFirst($graphResidual->getVertex($idA));
try {
$pathFlow = $alg->getWalkTo($graphResidual->getVertex($idB));
} catch (OutOfBoundsException $e) {
$pathFlow = NULL;
}
// If path exists add the new flow to graph
if ($pathFlow) {
// 2. get max flow from path
$maxFlowValue = $pathFlow->getEdges()->getEdgeOrder(Edges::ORDER_CAPACITY)->getCapacity();
// 3. add flow to path
foreach ($pathFlow->getEdges() as $edge) {
// try to look for forward edge to increase flow
try {
$originalEdge = $graphResult->getEdgeClone($edge);
$originalEdge->setFlow($originalEdge->getFlow() + $maxFlowValue);
// forward edge not found, look for back edge to decrease flow
} catch (UnderflowException $e) {
$originalEdge = $graphResult->getEdgeCloneInverted($edge);
$originalEdge->setFlow($originalEdge->getFlow() - $maxFlowValue);
}
}
}
// repeat while we still finds paths with residual capacity to add flow to
} while ($pathFlow);
return $graphResult;
}
/**
* expect exception for edges with no capacity
* @expectedException UnexpectedValueException
*/
public function testInvalidNoCapacity()
{
$graph = new Graph();
$graph->createVertex()->createEdgeTo($graph->createVertex())->setFlow(1);
$alg = new ResidualGraph($graph);
$alg->createGraph();
}
/**
* @uses Graph::createGraphClone()
* @uses ResidualGraph::createGraph()
* @uses SpMooreBellmanFord::getEdgesTo(Vertex $targetVertex)
* @see Base::createGraph()
*/
public function createGraph()
{
$this->checkBalance();
$resultGraph = $this->graph->createGraphClone();
// initial balance to 0
$vertices = $resultGraph->getVertices();
foreach ($vertices as $vertex) {
$vertex->setBalance(0);
}
// initial flow of edges
$edges = $resultGraph->getEdges();
foreach ($edges as $edge) {
if (!$edge instanceof EdgeDirected) {
throw new UnexpectedValueException('Undirected edges are not supported for SuccessiveShortestPath');
}
// 0 if weight of edge is positive
$flow = 0;
// maximal flow if weight of edge is negative
if ($edge->getWeight() < 0) {
$flow = $edge->getCapacity();
$startVertex = $edge->getVertexStart();
$endVertex = $edge->getVertexEnd();
// add balance to start- and end-vertex
$this->addBalance($startVertex, $flow);
$this->addBalance($endVertex, -$flow);
}
$edge->setFlow($flow);
}
// return or Exception inside this while
while (true) {
// create residual graph
$algRG = new ResidualGraph($resultGraph);
$residualGraph = $algRG->createGraph();
// search for a source
try {
$sourceVertex = $this->getVertexSource($residualGraph);
} catch (UnderflowException $ignore) {
// no source is found => minimum-cost flow is found
break;
}
// search for reachable target sink from this source
try {
$targetVertex = $this->getVertexSink($sourceVertex);
} catch (UnderflowException $e) {
// no target found => network does not have enough capacity
throw new UnexpectedValueException('The graph has not enough capacity for the minimum-cost flow', 0, $e);
}
// calculate shortest path between source- and target-vertex
$algSP = new SpMooreBellmanFord($sourceVertex);
$edgesOnFlow = $algSP->getEdgesTo($targetVertex);
// calculate the maximal possible flow
// new flow is the maximal possible flow for this path
$newflow = $this->graph->getVertex($sourceVertex->getId())->getBalance() - $sourceVertex->getBalance();
$targetFlow = -($this->graph->getVertex($targetVertex->getId())->getBalance() - $targetVertex->getBalance());
// get minimum of source and target
if ($targetFlow < $newflow) {
$newflow = $targetFlow;
}
// get minimum of capacity remaining on path
$minCapacity = $edgesOnFlow->getEdgeOrder(Edges::ORDER_CAPACITY_REMAINING)->getCapacityRemaining();
if ($minCapacity < $newflow) {
$newflow = $minCapacity;
}
// add the new flow to the path
$this->addFlow($resultGraph, $edgesOnFlow, $newflow);
// add balance to source and remove for the target sink
$oriSourceVertex = $resultGraph->getVertex($sourceVertex->getId());
$oriTargetVertex = $resultGraph->getVertex($targetVertex->getId());
$this->addBalance($oriSourceVertex, $newflow);
$this->addBalance($oriTargetVertex, -$newflow);
}
return $resultGraph;
}