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Merge pull request #48 from pankaj-bind/AIEdmondsKarpTest
Added Edmonds-Karp Algorithm Implementation
2 parents ea1fd39 + 2ff6e9e commit b99ea4e

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‎src/AI-Algorithms-Graph-Components/AINetworkFlowEdge.class.st‎

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@@ -43,3 +43,9 @@ AINetworkFlowEdge >> flow: anObject [
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AINetworkFlowEdge >> initialize [
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flow:=0
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]
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{ #category : 'accessing' }
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AINetworkFlowEdge >> residualCapacity [
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"Return the residual capacity of this edge"
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^ capacity - flow
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]

‎src/AI-Algorithms-Graph-Tests/AIEdmondsKarpTest.class.st‎

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"
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Test class for the Edmonds-Karp algorithm
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"
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Class {
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#name : 'AIEdmondsKarpTest',
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#superclass : 'TestCase',
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#category : 'AI-Algorithms-Graph-Tests',
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#package : 'AI-Algorithms-Graph-Tests'
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}
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{ #category : 'tests' }
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AIEdmondsKarpTest >> testBasicMaxFlow [
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"Test basic maximum flow computation"
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| nodes edges edmondsKarp maxFlow |
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nodes := #( $s $a $b $t ).
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edges := #( #( $s $a 10 ) #( $s $b 8 ) #( $a $b 5 ) #( $a $t 10 ) #( $b $t 10 ) ).
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edmondsKarp := AIEdmondsKarp new.
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edmondsKarp nodes: nodes.
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edmondsKarp
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edges: edges
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from: [ :each | each first ]
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to: [ :each | each second ]
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capacity: [ :each | each third ].
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edmondsKarp source: $s sink: $t.
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maxFlow := edmondsKarp run.
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self assert: maxFlow equals: 18
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]
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{ #category : 'tests' }
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AIEdmondsKarpTest >> testComplexNetwork [
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"Test with a more complex flow network"
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| nodes edges edmondsKarp maxFlow |
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nodes := #( 1 2 3 4 5 6 ).
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edges := #(
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#( 1 2 16 ) #( 1 3 13 )
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#( 2 3 10 ) #( 2 4 12 )
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#( 3 2 4 ) #( 3 5 14 )
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#( 4 3 9 ) #( 4 6 20 )
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#( 5 4 7 ) #( 5 6 4 ) ).
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edmondsKarp := AIEdmondsKarp new.
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edmondsKarp nodes: nodes.
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edmondsKarp
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edges: edges
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from: [ :each | each first ]
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to: [ :each | each second ]
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capacity: [ :each | each third ].
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edmondsKarp source: 1 sink: 6.
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maxFlow := edmondsKarp run.
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self assert: maxFlow equals: 23
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]
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{ #category : 'tests' }
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AIEdmondsKarpTest >> testNoPath [
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"Test when there's no path from source to sink"
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| nodes edges edmondsKarp maxFlow |
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nodes := #( $a $b $c $d ).
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edges := #( #( $a $b 5 ) #( $c $d 3 ) ).
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edmondsKarp := AIEdmondsKarp new.
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edmondsKarp nodes: nodes.
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edmondsKarp
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edges: edges
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from: [ :each | each first ]
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to: [ :each | each second ]
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capacity: [ :each | each third ].
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edmondsKarp source: $a sink: $d.
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maxFlow := edmondsKarp run.
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self assert: maxFlow equals: 0
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]
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{ #category : 'tests' }
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AIEdmondsKarpTest >> testSingleEdge [
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"Test with a single edge from source to sink"
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| nodes edges edmondsKarp maxFlow |
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nodes := #( $s $t ).
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edges := #( #( $s $t 15 ) ).
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edmondsKarp := AIEdmondsKarp new.
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edmondsKarp nodes: nodes.
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edmondsKarp
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edges: edges
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from: [ :each | each first ]
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to: [ :each | each second ]
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capacity: [ :each | each third ].
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edmondsKarp source: $s sink: $t.
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maxFlow := edmondsKarp run.
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self assert: maxFlow equals: 15
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]

‎src/AI-Algorithms-Graph/AIEdmondsKarp.class.st‎

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"
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The Edmonds-Karp algorithm is an implementation of the Ford-Fulkerson method for computing the maximum flow in a flow network. It uses breadth-first search to find the shortest augmenting path from source to sink in terms of the number of edges.
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The algorithm works by:
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1. Initialize flow to 0 for all edges
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2. While there exists an augmenting path from source to sink:
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a. Find the shortest augmenting path using BFS
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b. Find the minimum residual capacity along this path
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c. Update the flow along this path
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3. Return the maximum flow value
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Time complexity: O(VE²) where V is the number of vertices and E is the number of edges.
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Example usage:
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|nodes edges edmondsKarp maxFlow|
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nodes := #( $s $a $b $t ).
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edges := #( #( $s $a 10 ) #( $s $b 8 ) #( $a $b 5 ) #( $a $t 10 ) #( $b $t 10 ) ).
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edmondsKarp := AIEdmondsKarp new.
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edmondsKarp nodes: nodes.
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edmondsKarp
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edges: edges
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from: [ :each | each first ]
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to: [ :each | each second ]
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capacity: [ :each | each third ].
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edmondsKarp source: $s sink: $t.
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maxFlow := edmondsKarp run.
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"
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Class {
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#name : 'AIEdmondsKarp',
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#superclass : 'AIGraphAlgorithm',
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#instVars : [
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'source',
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'sink',
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'parent'
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],
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#category : 'AI-Algorithms-Graph-Maximum Flow',
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#package : 'AI-Algorithms-Graph',
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#tag : 'Maximum Flow'
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}
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{ #category : 'configuration' }
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AIEdmondsKarp >> edgeClass [
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^ AINetworkFlowEdge
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]
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{ #category : 'building - graph' }
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AIEdmondsKarp >> edges: aCollection from: source to: target capacity: capacityFunction [
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| edge reverseEdge |
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aCollection do: [ :eModel |
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edge := self addEdge: eModel from: source to: target.
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edge ifNotNil: [
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edge capacity: (capacityFunction value: eModel).
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edge flow: 0 ].
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"Add reverse edge with 0 capacity for residual graph"
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reverseEdge := self addEdge: eModel from: target to: source.
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reverseEdge ifNotNil: [
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reverseEdge capacity: 0.
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reverseEdge flow: 0 ] ]
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]
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{ #category : 'private' }
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AIEdmondsKarp >> findAugmentingPathBFS [
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"Find an augmenting path from source to sink using BFS.
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Returns true if a path exists, false otherwise.
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Updates the parent array to reconstruct the path."
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| queue visited |
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queue := LinkedList new.
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visited := Set new.
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parent := Dictionary new.
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queue addLast: source.
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visited add: source.
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[ queue isNotEmpty ] whileTrue: [
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| current |
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current := queue removeFirst.
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current = sink ifTrue: [ ^ true ].
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current outgoingEdges do: [ :edge |
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| neighbor residualCapacity |
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neighbor := edge to.
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residualCapacity := edge capacity - edge flow.
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(visited includes: neighbor) not & (residualCapacity > 0) ifTrue: [
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queue addLast: neighbor.
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visited add: neighbor.
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parent at: neighbor put: edge ] ] ].
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^ false
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]
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{ #category : 'private' }
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AIEdmondsKarp >> findBottleneckCapacity [
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"Find the minimum residual capacity along the augmenting path"
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| current minCapacity |
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current := sink.
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minCapacity := Float infinity.
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[ current ~= source ] whileTrue: [
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| edge residualCapacity |
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edge := parent at: current.
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residualCapacity := edge capacity - edge flow.
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minCapacity := minCapacity min: residualCapacity.
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current := edge from ].
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^ minCapacity
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]
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{ #category : 'private' }
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AIEdmondsKarp >> findReverseEdge: anEdge [
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"Find the reverse edge for the given edge"
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^ anEdge to outgoingEdges
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detect: [ :edge | edge to = anEdge from ]
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ifNone: [ nil ]
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]
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{ #category : 'initialization' }
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AIEdmondsKarp >> initialize [
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super initialize.
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parent := Dictionary new
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]
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{ #category : 'configuration' }
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AIEdmondsKarp >> nodeClass [
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^ AIPathDistanceNode
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]
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{ #category : 'running' }
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AIEdmondsKarp >> run [
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"Execute the Edmonds-Karp algorithm and return the maximum flow value"
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| maxFlow pathFlow |
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maxFlow := 0.
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[ self findAugmentingPathBFS ] whileTrue: [
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pathFlow := self findBottleneckCapacity.
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self updateFlowAlongPath: pathFlow.
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maxFlow := maxFlow + pathFlow ].
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^ maxFlow
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]
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{ #category : 'accessing' }
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AIEdmondsKarp >> source: sourceNode sink: sinkNode [
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source := self findNode: sourceNode.
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sink := self findNode: sinkNode
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]
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{ #category : 'private' }
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AIEdmondsKarp >> updateFlowAlongPath: flowValue [
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"Update the flow along the augmenting path found by BFS"
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| current |
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current := sink.
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[ current ~= source ] whileTrue: [
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| edge reverseEdge |
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edge := parent at: current.
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"Update forward edge flow"
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edge flow: edge flow + flowValue.
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"Update reverse edge flow"
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reverseEdge := self findReverseEdge: edge.
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reverseEdge flow: reverseEdge flow - flowValue.
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current := edge from ]
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]

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