New: Reduction from Matching to Set Packing (#129)

* save

* New:Reduction from Matching to Set Packing

Author: c-allergic

src/ProblemReductions.jl

@@ -45,6 +45,7 @@ export ReductionSATToIndependentSet, ReductionSATToDominatingSet
 export ReductionIndependentSetToSetPacking, ReductionSetPackingToIndependentSet
 export ReductionSATToCircuit
 export ReductionIndependentSetToVertexCovering
+export ReductionMatchingToSetPacking
 
 # reduction path
 export ReductionGraph, reduction_graph, reduction_paths, ConcatenatedReduction

src/rules/matching_setpacking.jl

@@ -0,0 +1,31 @@
+"""
+$TYPEDEF
+The reduction result of a vertex matching to a set packing problem.
+
+### Fields
+- `SetPacking{WT<:AbstractVector{Int}}`: the target set packing problem
+"""
+struct ReductionMatchingToSetPacking{ET,T,WT<:AbstractVector{T}} <: AbstractReductionResult
+    setpacking::SetPacking{ET, T, WT}
+end
+Base.:(==)(a::ReductionMatchingToSetPacking, b::ReductionMatchingToSetPacking) = a.setpacking == b.setpacking
+
+target_problem(res::ReductionMatchingToSetPacking) = res.setpacking
+
+function reduceto(::Type{SetPacking}, s::Matching)
+    sp = matching2setpacking(s.graph, s.weights)
+    return ReductionMatchingToSetPacking(sp)
+end
+
+function matching2setpacking(g::SimpleGraph, weights)
+    subsets = Vector{Vector{Int}}()
+    # map edges to subset
+    for edge in edges(g)
+        push!(subsets,[edge.src, edge.dst])
+    end
+    return SetPacking(subsets, weights)
+end
+
+function extract_solution(res::ReductionMatchingToSetPacking, sol)
+    return sol
+end

src/rules/rules.jl

@@ -87,4 +87,5 @@ include("sat_independentset.jl")
 include("sat_dominatingset.jl")
 include("independentset_setpacking.jl")
 include("circuit_sat.jl")
-include("vertexcovering_independentset.jl")
+include("vertexcovering_independentset.jl")
+include("matching_setpacking.jl")

test/rules/matching_setpacking.jl

@@ -0,0 +1,29 @@
+using Test, ProblemReductions, Graphs
+
+@testset "matching_setpacking" begin
+
+    # UnitWeight Graph
+    g1 = SimpleGraph(4)
+    for (i, j) in [(1, 2), (1, 3), (3, 4), (2, 3)]
+        add_edge!(g1, i, j)
+    end
+    Matching1 = Matching(g1)
+    SP1 = reduceto(SetPacking, Matching1)
+    @test target_problem(SP1) == SP1.setpacking
+    @test target_problem(SP1) == SetPacking([[1,2], [1,3],[2,3] ,[3,4]], [1, 1, 1, 1])
+    sol = findbest(SP1.setpacking, BruteForce())
+    @test extract_solution(SP1, sol) == sol
+
+    # Weighted Graph
+    g2 = SimpleGraph(4)
+    for (i, j) in [(1, 2), (1, 3), (3, 4), (2, 3)]
+        add_edge!(g2, i, j)
+    end
+    Matching2 = Matching(g2, [1, 2, 3, 4])
+    SP2 = reduceto(SetPacking, Matching2)
+    @test target_problem(SP2) == SP2.setpacking
+    @test target_problem(SP2) == SetPacking([[1,2], [1,3], [2,3], [3,4]], [1, 2, 3, 4])
+    sol1 = findbest(SP2.setpacking, BruteForce())
+    sol2 = findbest(Matching2,BruteForce())
+    @test extract_solution(SP2, sol1) == sol2
+end

test/rules/rules.jl

@@ -48,6 +48,10 @@ end
     include("vertexcovering_independentset.jl")
 end
 
+@testset "matching_setpacking" begin
+    include("matching_setpacking.jl")
+end
+
 @testset "rules" begin
     circuit = CircuitSAT(@circuit begin
         x = a ∨ ¬b
@@ -65,6 +69,7 @@ end
     is = IndependentSet(graph)
     is2 = IndependentSet(graph2)
     setpacking = SetPacking([[1, 2, 5], [1, 3], [2, 4], [3, 6], [2, 3, 6]])
+    matching = Matching(graph)
     for (source, target_type) in [
             # please add more tests here
             circuit => SpinGlass{<:SimpleGraph},
@@ -83,6 +88,7 @@ end
             is2 => SetPacking,
             setpacking => IndependentSet{<:SimpleGraph},
             is => VertexCovering,
+            matching => SetPacking
         ]
         @info "Testing reduction from $(typeof(source)) to $(target_type)"
         # directly solve