New model:Clique Cover

src/ProblemReductions.jl

@@ -32,6 +32,7 @@ export MaximalIS
 export PaintShop
 export BinaryMatrixFactorization, is_binary_matrix_factorization
 export BicliqueCover, is_biclique_cover
+export CliqueCover,is_clique_cover
 
 # rules
 export target_problem, AbstractProblem, ConstraintSatisfactionProblem, solution_size, solution_size_multiple, SolutionSize, objectives, constraints, energy_mode

src/models/CliqueCover.jl

@@ -0,0 +1,60 @@
+"""
+$TYPEDEF
+    CliqueCover{K}(graph::SimpleGraph{Int64}, k::Int64)
+
+A clique cover of a graph G is a set of cliques such that all vertices in G is coverd by the vertices union of these cliques. A K clique cover is to find whether we could use only k cliques to cover all the vertices in the graph.
+
+"""
+struct CliqueCover{Int64} <: ConstraintSatisfactionProblem{Int64}
+    graph::SimpleGraph{Int64}
+    k::Int64
+    function CliqueCover(graph::SimpleGraph{Int64}, k::Int64)
+        new{Int64}(graph, k)
+    end
+end
+problem_size(c::CliqueCover) = (; num_vertices=nv(c.graph), num_edges=ne(c.graph), k=c.k)
+num_variables(c::CliqueCover) = nv(c.graph) * c.k
+num_flavors(::Type{<:CliqueCover}) = 2
+
+# constraints interface
+function constraints(c::CliqueCover)
+    return [LocalConstraint(num_flavors(c), v, [0,1]) for v in vertices(c.graph)]
+end
+function objectives(c::CliqueCover)
+    return [LocalSolutionSize(num_flavors(c), [v], [0, 1]) for v in vertices(c.graph)]
+end
+energy_mode(::Type{<:CliqueCover}) = SmallerSizeIsBetter()
+
+function is_clique_cover(configs::Vector{Vector{Int64}}, c::CliqueCover)
+    # check if the number of cliques is equal to k
+    if length(configs) != c.k
+        print(1)
+        return false
+    end
+    # check if they are all valid clique
+    if any(config -> !is_clique(c, config), configs)
+        print(2)
+        return false
+    end
+    vertices_covered = reduce(vcat, [findall(x-> x==1,config) for config in configs])
+    # check if the vertices are covered by the cliques
+    if length(vertices_covered) != nv(c.graph)
+        print(3)
+        return false
+    end
+    return true
+end
+function is_clique(c::CliqueCover,config::Vector{Int64})
+    vertices = findall(x -> x == 1, config)
+    for (v1, v2) in collect(Iterators.product(vertices, vertices))
+        # pass if the vertices are the same
+        if v1 == v2
+            continue
+        end
+        # check if the edge exists in the graph, if not, return false
+        if !has_edge(c.graph, v1, v2)
+            return false
+        end
+    end
+    return true
+end

src/models/models.jl

@@ -376,3 +376,4 @@ include("MaximalIS.jl")
 include("Paintshop.jl")
 include("BicliqueCover.jl")
 include("BMF.jl")
+include("CliqueCover.jl")

test/models/CliqueCover.jl

@@ -0,0 +1,33 @@
+using Test, ProblemReductions, Graphs
+
+@testset "CliqueCover" begin
+    g = SimpleGraph(5)
+    for (i,j) in [(1,3),(1,5),(2,3),(2,4),(3,5)]
+        add_edge!(g,i,j)
+    end
+    c = CliqueCover(g,2)
+    @test num_variables(c) == 5 * 2
+    @test num_flavors(c) == 2
+    @test problem_size(c) == (; num_vertices=5, num_edges=5, k=2)
+    @test Base.:(==)(c, CliqueCover(g,2))
+    @test energy_mode(c) == SmallerSizeIsBetter()
+    @test is_clique_cover([[1,0,1,0,1],[0,1,0,1,0]],c) == true
+    @test is_clique_cover([[1,0,1,0,0],[0,1,0,1,0],[0,0,0,0,0]],c) == false
+    @test is_clique_cover([[1,0,1,0,0],[0,1,0,1,1]],c) == false
+    @test ProblemReductions.is_clique(c,[1,0,1,0,0]) == true
+    @test ProblemReductions.is_clique(c,[0,1,0,1,1]) == false
+    @test ProblemReductions.is_clique(c,[1,0,1,0,1]) == true
+
+    g1 = SimpleGraph(6)
+    for (i,j) in [(1,3),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(4,6),(5,6)]
+        add_edge!(g1,i,j)
+    end
+    c1 = CliqueCover(g1,2)
+    @test is_clique_cover([[1,0,0,0,1,1],[0,1,1,1,0,0]],c1) == true
+    @test is_clique_cover([[1,0,1,0,1,0],[0,1,0,1,0,0]],c1) == false
+    @test is_clique_cover([[1,0,1,0,1,0],[0,1,0,1,0,0],[0,0,0,0,0,0]],c1) == false
+    @test ProblemReductions.is_clique(c1,[1,0,1,0,1,0]) == true
+    c2 = CliqueCover(g1,3)
+    @test is_clique_cover([[1,0,1,0,1,0],[0,1,0,1,0,0],[0,0,0,0,0,1]],c2) == true
+    @test is_clique_cover([[1,0,1,0,1,0],[0,1,0,1,0,0],[0,0,0,0,0,0]],c2) == false
+end

test/models/models.jl

@@ -74,3 +74,6 @@ end
     include("BicliqueCover.jl")
 end
 
+@testset "CliqueCover" begin
+    include("CliqueCover.jl")
+end