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Merge pull request #73 from clue/improve-minimumspanningtree
Improve Algorithm\MinimumSpanningTree
2 parents 6eb0496 + 79ab285 commit 3e61948

7 files changed

Lines changed: 281 additions & 57 deletions

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‎CHANGELOG.md‎

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@@ -81,6 +81,18 @@ you spot any mistakes.
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* Feature: Support opening GraphViz images on Mac OS X in default image viewer
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([#67](https://github.com/clue/graph/issues/67) @onigoetz)
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* Feature: Add `Algorithm\MinimumSpanningTree\Base::getWeight()` to get total
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weight of resulting minimum spanning tree (MST).
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([#73](https://github.com/clue/graph/issues/73))
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* Feature: Each `Algorithm\MinimumSpanningTree` algorithm now supports
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undirected and mixed Graphs, as well as null weights for Edges.
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([#73](https://github.com/clue/graph/issues/73))
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* BC break: Each `Algorithm\MinimumSpanningTree` algorithm now throws an
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`UnexpectedValueException` for unconnected Graphs (and thus also null Graphs).
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([#73](https://github.com/clue/graph/issues/73))
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* Feature: Add `Walk::factoryFromVertices()`
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([#64](https://github.com/clue/graph/issues/64)).
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‎lib/Fhaculty/Graph/Algorithm/MinimumSpanningTree/Base.php‎

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@@ -4,28 +4,88 @@
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use Fhaculty\Graph\Algorithm\Base as AlgorithmBase;
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use Fhaculty\Graph\Set\Edges;
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use Fhaculty\Graph\Edge\Directed as EdgeDirected;
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use Fhaculty\Graph\Edge\Base as Edge;
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use SplPriorityQueue;
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/**
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* Abstract base class for minimum spanning tree (MST) algorithms
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*
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* A minimum spanning tree of a graph is a subgraph that is a tree and connects
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* all the vertices together while minimizing the total sum of all edges'
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* weights.
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*
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* A spanning tree thus requires a connected graph (single connected component),
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* otherwise we can span multiple trees (spanning forest) within each component.
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* Because a null graph (a Graph with no vertices) is not considered connected,
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* it also can not contain a spanning tree.
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*
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* Most authors demand that the input graph has to be undirected, whereas this
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* library supports also directed and mixed graphs. The actual direction of the
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* edge will be ignored, only its incident vertices will be checked. This is
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* done in order to be consistent to how ConnectedComponents are checked.
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*
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* @link http://en.wikipedia.org/wiki/Minimum_Spanning_Tree
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* @link http://en.wikipedia.org/wiki/Spanning_Tree
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* @link http://mathoverflow.net/questions/120536/is-the-empty-graph-a-tree
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*/
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abstract class Base extends AlgorithmBase
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{
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/**
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* create new resulting graph with only edges on minimum spanning tree
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*
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* @return Graph
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* @uses AlgorithmMst::getEdges()
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* @uses self::getGraph()
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* @uses self::getEdges()
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* @uses Graph::createGraphCloneEdges()
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*/
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public function createGraph()
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{
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// Copy Graph
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return $this->getGraph()->createGraphCloneEdges($this->getEdges());
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}
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abstract protected function getGraph();
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/**
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* get all edges on minimum spanning tree
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*
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* @return Edges
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*/
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abstract public function getEdges();
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/**
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* return reference to current Graph
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*
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* @return Graph
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*/
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abstract protected function getGraph();
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/**
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* get total weight of minimum spanning tree
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*
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* @return float
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*/
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public function getWeight()
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{
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return $this->getEdges()->getSumCallback(function (Edge $edge) {
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return $edge->getWeight();
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});
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}
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/**
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* helper method to add a set of Edges to the given set of sorted edges
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*
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* @param Edges $edges
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* @param SplPriorityQueue $sortedEdges
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*/
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protected function addEdgesSorted(Edges $edges, SplPriorityQueue $sortedEdges)
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{
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// For all edges
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foreach ($edges as $edge) {
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/* @var $edge Edge */
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// ignore loops (a->a)
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if (!$edge->isLoop()) {
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// Add edges with negative weight because of order in stl
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$sortedEdges->insert($edge, -$edge->getWeight());
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}
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}
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}
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}

‎lib/Fhaculty/Graph/Algorithm/MinimumSpanningTree/Kruskal.php‎

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@@ -24,12 +24,6 @@ public function __construct(Graph $inputGraph)
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$this->graph = $inputGraph;
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}
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public function createGraph()
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{
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// Copy Graph
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return $this->graph->createGraphCloneEdges($this->getEdges());
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}
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protected function getGraph()
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{
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return $this->graph;
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$sortedEdges = new SplPriorityQueue();
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// For all edges
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foreach ($this->graph->getEdges() as $edge) {
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// ignore loops (a->a)
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if (!$edge->isLoop()) {
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if ($edge instanceof EdgeDirected) {
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throw new UnexpectedValueException('Kruskal for directed edges not supported');
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}
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$weight = $edge->getWeight();
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if ($weight === NULL) {
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throw new UnexpectedValueException('Kruskal for edges with no weight not supported');
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}
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// Add edges with negativ Weight because of order in stl
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$sortedEdges->insert($edge, - $weight);
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}
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}
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if ($sortedEdges->isEmpty()) {
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throw new RuntimeException('No edges found');
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}
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// $sortedEdges = $this->graph->getEdgesOrdered('weight');
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$this->addEdgesSorted($this->graph->getEdges(), $sortedEdges);
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$returnEdges = array();
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‎lib/Fhaculty/Graph/Algorithm/MinimumSpanningTree/Prim.php‎

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@@ -40,30 +40,22 @@ public function getEdges()
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// get unvisited vertex of the edge and add edges from new vertex
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// Add all edges from $currentVertex to priority queue
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foreach ($vertexCurrent->getEdges() as $currentEdge) {
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if (!$currentEdge->isLoop()) {
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if ($currentEdge instanceof EdgeDirected) {
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throw new UnexpectedValueException('Unable to create MST for directed graphs');
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}
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// Add edges to priority queue with inverted weights (priority queue has high values at the front)
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$edgeQueue->insert($currentEdge, -$currentEdge->getWeight());
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}
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}
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$this->addEdgesSorted($vertexCurrent->getEdges(), $edgeQueue);
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do {
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try {
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// Get next cheapest edge
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$cheapestEdge = $edgeQueue->extract();
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/* @var $cheapestEdge EdgeDirected */
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} catch (Exception $e) {
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return $returnEdges;
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throw new UnexpectedValueException('Graph has more than one component');
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throw new UnexpectedValueException('Graph has more than one component', 0, $e);
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}
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// Check if edge is between unmarked and marked edge
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$vertexA = $cheapestEdge->getVerticesStart()->getVertexFirst();
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$vertexB = $cheapestEdge->getVertexToFrom($vertexA);
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$vertices = $cheapestEdge->getVertices();
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$vertexA = $vertices->getVertexFirst();
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$vertexB = $vertices->getVertexLast();
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// Edge is between marked and unmared vertex
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} while (!(isset($markInserted[$vertexA->getId()]) XOR isset($markInserted[$vertexB->getId()])));

‎tests/Fhaculty/Graph/Algorithm/MinimumSpanningTree/BaseMstTest.php‎

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<?php
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use Fhaculty\Graph\Graph;
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use Fhaculty\Graph\Vertex;
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use Fhaculty\Graph\Loader\CompleteGraph as LoaderCompleteGraph;
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use Fhaculty\Graph\Algorithm\MinimumSpanningTree\Base as MstBase;
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abstract class BaseMstTest extends TestCase
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{
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/**
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* @param Vertex $vertex
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* @return MstBase
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*/
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abstract protected function createAlg(Vertex $vertex);
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public function testIsolatedVertex()
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{
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$graph = new Graph();
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$v1 = $graph->createVertex(1);
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$alg = $this->createAlg($v1);
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$this->assertCount(0, $alg->getEdges());
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$this->assertEquals(0, $alg->getWeight());
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$graphMst = $alg->createGraph();
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$this->assertGraphEquals($graph, $graphMst);
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}
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public function testSingleEdge()
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{
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// 1 --[3]-- 2
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$graph = new Graph();
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$v1 = $graph->createVertex(1);
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$v2 = $graph->createVertex(2);
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$v1->createEdge($v2)->setWeight(3);
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$alg = $this->createAlg($v1);
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$this->assertCount(1, $alg->getEdges());
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$this->assertEquals(3, $alg->getWeight());
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$this->assertGraphEquals($graph, $alg->createGraph());
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}
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public function testSimpleGraph()
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{
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// 1 --[6]-- 2 --[9]-- 3 --[7]-- 4 --[8]-- 5
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$graph = new Graph();
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$v1 = $graph->createVertex(1);
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$v2 = $graph->createVertex(2);
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$v3 = $graph->createVertex(3);
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$v4 = $graph->createVertex(4);
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$v5 = $graph->createVertex(5);
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$v1->createEdge($v2)->setWeight(6);
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$v2->createEdge($v3)->setWeight(9);
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$v3->createEdge($v4)->setWeight(7);
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$v4->createEdge($v5)->setWeight(8);
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$alg = $this->createAlg($v1);
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62+
$graphMst = $alg->createGraph();
63+
$this->assertGraphEquals($graph, $graphMst);
64+
}
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public function testFindingCheapestEdge()
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{
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// /--[4]--\
69+
// / \
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// 1 ---[3]--- 2
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// \ /
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// \--[5]--/
73+
$graph = new Graph();
74+
$v1 = $graph->createVertex(1);
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$v2 = $graph->createVertex(2);
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$v1->createEdge($v2)->setWeight(4);
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$v1->createEdge($v2)->setWeight(3);
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$v1->createEdge($v2)->setWeight(5);
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$alg = $this->createAlg($v1);
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$edges = $alg->getEdges();
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$this->assertCount(1, $edges);
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$this->assertEquals(3, $edges->getEdgeFirst()->getWeight());
85+
$this->assertEquals(3, $alg->getWeight());
86+
}
87+
88+
public function testFindingCheapestTree()
89+
{
90+
// 1 --[4]-- 2 --[5]-- 3
91+
// \ /
92+
// \-------[6]-----/
93+
$graph = new Graph();
94+
$v1 = $graph->createVertex(1);
95+
$v2 = $graph->createVertex(2);
96+
$v3 = $graph->createVertex(3);
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$v1->createEdge($v2)->setWeight(4);
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$v2->createEdge($v3)->setWeight(5);
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$v3->createEdge($v1)->setWeight(6);
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// 1 --[4]-- 2 -- [5] -- 3
102+
$graphExpected = new Graph();
103+
$ve1 = $graphExpected->createVertex(1);
104+
$ve2 = $graphExpected->createVertex(2);
105+
$ve3 = $graphExpected->createVertex(3);
106+
$ve1->createEdge($ve2)->setWeight(4);
107+
$ve2->createEdge($ve3)->setWeight(5);
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109+
$alg = $this->createAlg($v1);
110+
$this->assertCount(2, $alg->getEdges());
111+
$this->assertEquals(9, $alg->getWeight());
112+
$this->assertGraphEquals($graphExpected, $alg->createGraph());
113+
}
114+
115+
public function testMixedGraphDirectionIsIgnored()
116+
{
117+
// 1 --[6]-> 2 --[7]-- 3 --[8]-- 4 <-[9]-- 5
118+
$graph = new Graph();
119+
$v1 = $graph->createVertex(1);
120+
$v2 = $graph->createVertex(2);
121+
$v3 = $graph->createVertex(3);
122+
$v4 = $graph->createVertex(4);
123+
$v5 = $graph->createVertex(5);
124+
$v1->createEdgeTo($v2)->setWeight(6);
125+
$v2->createEdge($v3)->setWeight(7);
126+
$v4->createEdge($v3)->setWeight(8);
127+
$v5->createEdgeTo($v4)->setWeight(9);
128+
129+
$alg = $this->createAlg($v1);
130+
131+
$this->assertCount(4, $alg->getEdges());
132+
$this->assertEquals(30, $alg->getWeight());
133+
$this->assertGraphEquals($graph, $alg->createGraph());
134+
}
135+
136+
/**
137+
* @expectedException UnexpectedValueException
138+
*/
139+
public function testMultipleComponentsFail()
140+
{
141+
// 1 --[1]-- 2, 3 --[1]-- 4
142+
$graph = new Graph();
143+
$v1 = $graph->createVertex(1);
144+
$v2 = $graph->createVertex(2);
145+
$v3 = $graph->createVertex(3);
146+
$v4 = $graph->createVertex(4);
147+
$v1->createEdge($v2)->setWeight(1);
148+
$v3->createEdge($v4)->setWeight(1);
149+
150+
$alg = $this->createAlg($v1);
151+
$alg->getEdges();
152+
}
153+
154+
/**
155+
* @expectedException UnexpectedValueException
156+
*/
157+
public function testMultipleIsolatedVerticesFormMultipleComponentsFail()
158+
{
159+
// 1, 2
160+
$graph = new Graph();
161+
$v1 = $graph->createVertex(1);
162+
$v2 = $graph->createVertex(2);
163+
164+
$alg = $this->createAlg($v1);
165+
$alg->getEdges();
166+
}
167+
168+
169+
}

‎tests/Fhaculty/Graph/Algorithm/MinimumSpanningTree/KruskalTest.php‎

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<?php
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3+
use Fhaculty\Graph\Graph;
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use Fhaculty\Graph\Vertex;
5+
use Fhaculty\Graph\Algorithm\MinimumSpanningTree\Kruskal;
6+
7+
class KruskalTest extends BaseMstTest
8+
{
9+
protected function createAlg(Vertex $vertex)
10+
{
11+
return new Kruskal($vertex->getGraph());
12+
}
13+
14+
/**
15+
* @expectedException UnexpectedValueException
16+
*/
17+
public function testNullGraphIsNotConsideredToBeConnected()
18+
{
19+
$graph = new Graph();
20+
21+
$alg = new Kruskal($graph);
22+
$alg->getEdges();
23+
}
24+
}

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