Set covering (#39)

* Update src/models/Coloring.jl

Co-authored-by: Jinguo Liu <cacate0129@gmail.com>

* update comment

* New: "SetCovering" model

* New:"SetCovering" model

* Add: single test & Clean up

* New:"findbest" function in set covering

* Add: single test of terms

---------

Co-authored-by: Jinguo Liu <cacate0129@gmail.com>

src/models/SetCovering.jl

@@ -0,0 +1,80 @@
+"""
+$TYPEDEF
+
+The [set covering problem](https://queracomputing.github.io/GenericTensorNetworks.jl/dev/generated/SetCovering/).
+
+Positional arguments
+-------------------------------
+* `sets` is a vector of vectors, a collection of subsets of universe , each set is associated with a weight specified in `weights`.
+* `weights` are associated with sets.
+
+"""
+
+struct SetCovering{ET, WT<:Union{UnitWeight, Vector}} <: AbstractProblem
+    sets::Vector{Vector{ET}}
+    weights::WT
+    function SetCovering(sets::Vector{Vector{ET}}, weights::Union{UnitWeight, Vector}=UnitWeight()) where {ET}
+        @assert weights isa UnitWeight || length(weights) == length(sets)
+        new{ET, typeof(weights)}(sets, weights)
+    end
+end
+Base.:(==)(a::SetCovering, b::SetCovering) = a.sets == b.sets && a.weights == b.weights
+
+#variables interface
+variables(gp::SetCovering) = gp.sets
+num_variables(c::SetCovering) = length(c.sets)
+flavors(::Type{<:SetCovering}) = [0, 1] #whether the set is selected or not
+
+
+
+# weights interface
+parameters(c::SetCovering) = c.weights
+set_parameters(c::SetCovering, weights) = SetCovering(c.sets, weights)
+terms(gp::SetCovering) = [[i] for i=1:length(gp.sets)] # return the index of sets
+
+"""
+    evaluate(c::SetCovering, config)
+   
+evaluate the energy of the set covering configuration `config`, the energy is the
+sum of the weights of the sets that are selected. Config is a vector of boolean numbers.
+""" 
+
+function evaluate(c::SetCovering, config)
+    @assert length(config) == num_variables(c)
+    set_covering_energy(c.weights, config )
+end
+set_covering_energy(weights::AbstractVector, config) = sum(weights[i]*config[i] for i=1:length(weights))
+
+"""
+    findbest(c::SetCovering) -> Vector
+
+Find the best configurations of the `c` using the `method`. We offer bruteforce search as the default method.
+
+"""
+
+function findbest(c::SetCovering, method="bruteforce")
+    best = nothing
+    best_energy = Inf 
+    for config in Iterators.product((fill([0,1],num_variables(c)))...)
+        if sum(config) == 0
+            continue
+        end
+        if is_set_covering(c,config)
+            energy = evaluate(c,config)
+            if energy < best_energy
+                best = config
+                best_energy = energy
+            end
+        end
+    end
+    return best
+end
+
+"""
+    is_set_covering(sets::AbstractVector, config)
+
+Return true if `config` (a vector of boolean numbers as the mask of sets) is a set covering of `sets`.
+"""
+function is_set_covering(c::SetCovering, config)
+    return reduce(union,c.sets)==reduce(union,c.sets[i] for i in 1:length(config) if config[i]==1)
+end

src/models/models.jl

@@ -93,3 +93,4 @@ Base.eltype(::UnitWeight) = Int
 include("SpinGlass.jl")
 include("Circuit.jl")
 include("Coloring.jl")
+include("SetCovering.jl")

test/models/SetCovering.jl

@@ -0,0 +1,27 @@
+using Test, ProblemReductions, Graphs
+using ProblemReductions: SetCovering, variables, flavors, terms, evaluate, set_parameters, parameters,is_set_covering,set_covering_energy, findbest
+
+@testset "setcovering" begin
+    c = SetCovering([[1, 2], [2, 3], [2, 3, 4]], [1, 1, 2])
+    # constructor function
+    @test variables(c)==[[1,2],[2,3],[2,3,4]]
+    @test num_variables(c) == 3
+    @test flavors(SetCovering) == [0, 1]
+    @test terms(c) == [[1], [2], [3]]
+
+    # weights interface
+    @test parameters(c) == [1, 1, 2]
+    @test set_parameters(c, [1, 2, 3]) == SetCovering([[1, 2], [2, 3], [2, 3, 4]], [1, 2, 3])
+
+    # evaluate
+    @test evaluate(c, [0, 1, 1]) == 3
+    @test set_covering_energy([1, 1, 2], [0, 0, 1]) == 2
+    @test is_set_covering(c,[1,0,1]) == true
+    @test is_set_covering(c,[0,0,1]) == false
+
+    # findbest
+    @test findbest(c) == (1,0,1)
+    @test findbest(c, "bruteforce") == (1,0,1)
+    g = SetCovering([[1, 2], [1, 3, 4], [2, 3]], [1, 1, 2])
+    @test findbest(g) == (1,1,0)
+end

test/models/models.jl

@@ -10,4 +10,8 @@ end
 
 @testset "Coloring" begin
     include("Coloring.jl")
+end
+
+@testset "SetCovering" begin
+    include("SetCovering.jl")
 end