Mincut (#11)

* added mincut + tests

* added doc

Author: matbesancon

docs/make.jl

@@ -12,5 +12,6 @@ makedocs(
         "Maxflow algorithms" => "maxflow.md",
         "Multiroute flows"   => "multiroute.md",
         "Min-cost flows"   => "mincost.md",
+        "Min-cut"   => "mincut.md",
     ]
 )

docs/src/mincut.md

@@ -0,0 +1,7 @@
+## Min-cut
+
+```@autodocs
+Modules = [LightGraphsFlows]
+Pages = ["mincut.jl"]
+Order = [:function, :type]
+```

src/LightGraphsFlows.jl

@@ -19,9 +19,10 @@ include("multiroute_flow.jl")
 include("kishimoto.jl")
 include("ext_multiroute_flow.jl")
 include("mincost.jl")
+include("mincut.jl")
 
 export
 maximum_flow, EdmondsKarpAlgorithm, DinicAlgorithm, BoykovKolmogorovAlgorithm, PushRelabelAlgorithm,
-multiroute_flow, KishimotoAlgorithm, ExtendedMultirouteFlowAlgorithm, mincost_flow
+multiroute_flow, KishimotoAlgorithm, ExtendedMultirouteFlowAlgorithm, mincost_flow, mincut
 
 end

src/mincut.jl

@@ -0,0 +1,30 @@
+"""
+    mincut(flow_graph::lg.IsDirected, source::Integer, target::Integer, capacity_matrix::AbstractMatrix, algorithm::AbstractFlowAlgorithm)
+
+Compute the min-cut between `source` and `target` for the given graph.
+First computes the maxflow using `algorithm` and then builds the partition of the residual graph
+Returns a triplet `(part1, part2, flow)` with the partition containing the source, the partition containing the target (the rest) and the min-cut(max-flow) value
+"""
+function mincut(
+        flow_graph::lg.DiGraph,             # the input graph
+        source::Integer,                       # the source vertex
+        target::Integer,                       # the target vertex
+        capacity_matrix::AbstractMatrix,       # edge flow capacities
+        algorithm::AbstractFlowAlgorithm       # keyword argument for algorithm
+    )
+    flow, flow_matrix = maximum_flow(flow_graph, source, target, capacity_matrix, algorithm)
+    residual_matrix = spzeros(lg.nv(flow_graph),lg.nv(flow_graph))
+    for edge in lg.edges(flow_graph)
+        residual_matrix[edge.src,edge.dst] = max(0.0, capacity_matrix[edge.src,edge.dst] - flow_matrix[edge.src,edge.dst])
+    end
+    part1 = typeof(source)[]
+    queue = [source]
+    while !isempty(queue)
+        node = pop!(queue)
+        push!(part1, node)
+        dests = [dst for dst in 1:lg.nv(flow_graph) if residual_matrix[node,dst]>0.0 && dst ∉ part1]
+        append!(queue, dests)
+    end
+    part2 = [node for node in 1:lg.nv(flow_graph) if node ∉ part1]
+    return (part1, part2, flow)
+end

test/mincut.jl

@@ -0,0 +1,39 @@
+@testset "Mincut" begin
+
+    g = lg.CompleteDiGraph(5)
+    cap1 = [
+       0.0 2.0 2.0 0.0 0.0
+       0.0 0.0 0.0 0.0 3.0
+       0.0 1.0 0.0 3.0 0.0
+       0.0 0.0 0.0 0.0 1.0
+       0.0 0.0 0.0 0.0 0.0
+    ];
+    (part1, part2, value) = LightGraphsFlows.mincut(g,1,5,cap1,LightGraphsFlows.PushRelabelAlgorithm())
+    @test value ≈ 4.0
+    @test part1 == [1]
+    @test sort(part2) == collect(2:5)
+    cap2 = [
+       0.0 3.0 2.0 0.0 0.0
+       0.0 0.0 0.0 0.0 3.0
+       0.0 1.0 0.0 3.0 0.0
+       0.0 0.0 0.0 0.0 1.5
+       0.0 0.0 0.0 0.0 0.0
+    ];
+    (part1, part2, value) = LightGraphsFlows.mincut(g,1,5,cap2,LightGraphsFlows.PushRelabelAlgorithm())
+    @test value ≈ 4.5
+    @test sort(part1) == collect(1:4)
+    @test part2 == [5]
+
+    g2 = lg.DiGraph(5)
+    lg.add_edge!(g2,1,2)
+    lg.add_edge!(g2,1,3)
+    lg.add_edge!(g2,3,4)
+    lg.add_edge!(g2,3,2)
+    lg.add_edge!(g2,2,5)
+
+    (part1, part2, value) = LightGraphsFlows.mincut(g2,1,5,cap1,LightGraphsFlows.PushRelabelAlgorithm())
+    @test value ≈ 3.0
+    @test sort(part1) == [1,3,4]
+    @test sort(part2) == [2,5]    
+
+end

test/runtests.jl

@@ -16,7 +16,9 @@ for t in [
         "push_relabel",
         "maximum_flow",
         "multiroute_flow",
-        "mincost"]
+        "mincost",
+        "mincut",
+        ]
     tp = joinpath(testdir, "$(t).jl")
     include(tp)
 end