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 testGraphTriangleCycleIsNotBipartit()
{
// 1 -> 2 -> 3 -> 1
$graph = new Graph();
$v1 = $graph->createVertex(1)->setGroup(1);
$v2 = $graph->createVertex(2)->setGroup(2);
$v3 = $graph->createVertex(3)->setGroup(1);
$v1->createEdgeTo($v2);
$v2->createEdgeTo($v3);
$v3->createEdgeTo($v1);
$alg = new AlgorithmGroups($graph);
$this->assertEquals(array(1, 2), $alg->getGroups());
$this->assertEquals(2, $alg->getNumberOfGroups());
$this->assertTrue($alg->getVerticesGroup(123)->isEmpty());
$this->assertEquals(array(1 => $v1, 3 => $v3), $alg->getVerticesGroup(1)->getMap());
$this->assertFalse($alg->isBipartit());
}
/**
* create graphviz script representing this graph
*
* @param Graph $graph graph to display
* @return string
* @uses Directed::hasDirected()
* @uses Graph::getVertices()
* @uses Graph::getEdges()
*/
public function createScript(Graph $graph)
{
$alg = new Directed($graph);
$directed = $alg->hasDirected();
$script = ($directed ? 'di' : '') . 'graph G {' . self::EOL;
// add global attributes
$globals = array('graph' => 'graphviz.graph.', 'node' => 'graphviz.node.', 'edge' => 'graphviz.edge.');
foreach ($globals as $key => $prefix) {
$bag = new AttributeBagNamespaced($graph, $prefix);
if ($layout = $bag->getAttributes()) {
$script .= $this->formatIndent . $key . ' ' . $this->escapeAttributes($layout) . self::EOL;
}
}
$alg = new Groups($graph);
// only append group number to vertex label if there are at least 2 different groups
$showGroups = $alg->getNumberOfGroups() > 1;
if ($showGroups) {
$gid = 0;
$indent = str_repeat($this->formatIndent, 2);
// put each group of vertices in a separate subgraph cluster
foreach ($alg->getGroups() as $group) {
$script .= $this->formatIndent . 'subgraph cluster_' . $gid++ . ' {' . self::EOL . $indent . 'label = ' . $this->escape($group) . self::EOL;
foreach ($alg->getVerticesGroup($group)->getMap() as $vid => $vertex) {
$layout = $this->getLayoutVertex($vertex);
$script .= $indent . $this->escapeId($vid);
if ($layout) {
$script .= ' ' . $this->escapeAttributes($layout);
}
$script .= self::EOL;
}
$script .= ' }' . self::EOL;
}
} else {
$alg = new Degree($graph);
// explicitly add all isolated vertices (vertices with no edges) and vertices with special layout set
// other vertices wil be added automatically due to below edge definitions
foreach ($graph->getVertices()->getMap() as $vid => $vertex) {
$layout = $this->getLayoutVertex($vertex);
if ($layout || $alg->isVertexIsolated($vertex)) {
$script .= $this->formatIndent . $this->escapeId($vid);
if ($layout) {
$script .= ' ' . $this->escapeAttributes($layout);
}
$script .= self::EOL;
}
}
}
$edgeop = $directed ? ' -> ' : ' -- ';
// add all edges as directed edges
foreach ($graph->getEdges() as $currentEdge) {
$both = $currentEdge->getVertices()->getVector();
$currentStartVertex = $both[0];
$currentTargetVertex = $both[1];
$script .= $this->formatIndent . $this->escapeId($currentStartVertex->getId()) . $edgeop . $this->escapeId($currentTargetVertex->getId());
$layout = $this->getLayoutEdge($currentEdge);
// this edge also points to the opposite direction => this is actually an undirected edge
if ($directed && $currentEdge->isConnection($currentTargetVertex, $currentStartVertex)) {
$layout['dir'] = 'none';
}
if ($layout) {
$script .= ' ' . $this->escapeAttributes($layout);
}
$script .= self::EOL;
}
$script .= '}' . self::EOL;
return $script;
}
/**
* checks whether the input graph's vertex groups are a valid bipartition
*
* @return boolean
* @uses AlgorithmGroups::isBipartit()
*/
public function isBipartitGroups()
{
$alg = new Groups($this->graph);
return $alg->isBipartit();
}