Add a new type: Dominating Set problem (without weights)

src/ProblemReductions.jl

@@ -20,6 +20,7 @@ export Coloring, coloring_energy, is_vertex_coloring
 export SetCovering, is_set_covering, set_covering_energy
 export BoolVar, CNFClause, CNF, Satisfiability, is_kSAT, satisfiable
 export MaxCut
+export DominatingSet
 
 # rules
 export target_problem, AbstractProblem, AbstractReductionResult, reduceto, extract_solution, reduction_complexity

src/models/DominatingSet.jl

@@ -0,0 +1,42 @@
+"""
+$TYPEDEF
+    DominatingSet(graph; weights=UnitWeight())
+
+The [dominating set](https://queracomputing.github.io/GenericTensorNetworks.jl/dev/generated/DominatingSet/) problem.
+
+Positional arguments
+-------------------------------
+* `graph` is the problem graph.
+
+We don't have weights for this problem.
+"""
+struct DominatingSet{ GT<:AbstractGraph} <: AbstractProblem
+    graph::GT
+    function DominatingSet( graph::AbstractGraph)
+        return new{typeof(graph)}(graph)
+    end
+end
+Base.:(==)(a::DominatingSet, b::DominatingSet) = ( a.graph == b.graph )
+
+# Variables Interface
+variables(gp::DominatingSet) = [1:nv(gp.graph)...]
+flavors(::Type{<:DominatingSet}) = [0, 1]
+
+"""
+    evaluate(c::DominatingSet, config)
+
+Firstly, we count the number of vertices outside the dominating set and the neighbours of the dominating set: 
+If this number is zero, this configuration corresponds to a dominating set. 
+* If the configuration is not a dominating set return Inf;
+* If the configuration is a dominating set return size(dominating set).
+"""
+
+function evaluate(c::DominatingSet, config)
+    g = c.graph
+    num_outside_vertices = count(w -> config[w] == 0 && all(v-> config[v] == 0, neighbors(g, w)), Graphs.vertices(g))
+    if num_outside_vertices == 0
+        return count(x -> x == 1, config)
+    else
+        return Inf
+    end
+end

src/models/models.jl

@@ -84,3 +84,4 @@ include("Coloring.jl")
 include("Satisfiability.jl")
 include("SetCovering.jl")
 include("MaxCut.jl")
+include("DominatingSet.jl")

test/models/DominatingSet.jl

@@ -0,0 +1,37 @@
+using Test, ProblemReductions, Graphs
+
+@testset "dominatingset" begin
+    # construct two equivalent graphs
+    g01 = SimpleGraph(5)
+    add_edge!(g01, 1, 2)
+    add_edge!(g01, 2, 3)
+    add_edge!(g01, 3, 4)
+    add_edge!(g01, 4, 5)
+
+    g02 = SimpleGraph(5)
+    add_edge!(g02, 4, 5)
+    add_edge!(g02, 1, 2)
+    add_edge!(g02, 3, 4)
+    add_edge!(g02, 2, 3)
+
+    # construct corresponding DominatingSet problems
+    DS_01 = DominatingSet(g01)
+    DS_02 = DominatingSet(g02)
+    @test DS_01 == DS_02
+
+    # variables
+    @test variables(DS_01) == [1, 2, 3, 4, 5]
+    @test num_variables(DS_01) == 5
+    @test flavors(DominatingSet) == [0, 1]
+
+    # evaluate
+    # Positive examples
+    @test evaluate(DS_01, [1, 0, 1, 0, 1]) == 3
+    @test evaluate(DS_01, [0, 1, 0, 1, 0]) == 2
+    @test evaluate(DS_01, [1, 1, 1, 1, 0]) == 4
+    # Negative examples
+    @test evaluate(DS_01, [0, 1, 1, 0, 0]) == Inf
+    @test evaluate(DS_01, [1, 0, 0, 0, 1]) == Inf
+    # findbest function
+    @test findbest(DS_01, BruteForce()) == [[1, 0, 0, 1, 0], [0, 1, 0, 1, 0], [0, 1, 0, 0, 1]]
+end

test/models/models.jl

@@ -22,4 +22,8 @@ end
 
 @testset "Maxcut" begin
     include("MaxCut.jl")
+end
+
+@testset "DominatingSet" begin
+    include("DominatingSet.jl")
 end

test/rules/rules.jl

@@ -4,7 +4,7 @@ using Test, ProblemReductions, Graphs
     include("spinglass_sat.jl")
 end
 
-@testset "spinglass_sat" begin
+@testset "spinglass_maxcut" begin
     include("spinglass_maxcut.jl")
 end