set packing

Author: GiggleLiu

notebooks/tutorial.jl

@@ -11,6 +11,9 @@ begin
 	using Revise, GraphTensorNetworks
 end
 
+# ╔═╡ 6c7f88d2-2491-4272-b0b6-83fe7778f81a
+md"## High level interfaces"
+
 # ╔═╡ 83fc0a3c-ef51-4d5c-9c46-baa645f80fd2
 locs = [rand(2) for i=1:70];
 
@@ -23,15 +26,21 @@ vizconfig(g; locs=locs, unit=0.5)
 # ╔═╡ b6e916e2-7d43-4085-a3c8-5c57069e8384
 gp = Independence(g; optmethod=:auto);
 
+# ╔═╡ 1a58dea3-14fa-4be7-b087-45ed9bad2407
+gp
+
 # ╔═╡ 03840394-3a5b-4c24-8b52-15f7e400f900
 timespace_complexity(gp)
 
 # ╔═╡ 11c71de9-caa9-40c6-84cb-a0f29d873805
-results = solutions(gp, CountingTropical{Float64}; all=false)
+results = solve(gp, "config max"; usecuda=false)
 
 # ╔═╡ edfc5600-9a4a-4657-b165-8eb3e8540edf
 vizconfig(g; locs=locs, unit=0.5, config=results[].c.data)
 
+# ╔═╡ 47e7a144-44c0-4770-8f82-1292b0aad8bc
+md"## Lower level interfaces"
+
 # ╔═╡ 3666f629-7a87-4b50-aaf1-cc128d598aaf
 md"## Different Algebras"
 
@@ -150,13 +159,16 @@ one(typeof(ce2))
 
 # ╔═╡ Cell order:
 # ╠═54d71646-ffad-11eb-3866-5f1c0bc5d0bf
+# ╟─6c7f88d2-2491-4272-b0b6-83fe7778f81a
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 # ╠═b6e916e2-7d43-4085-a3c8-5c57069e8384
+# ╠═1a58dea3-14fa-4be7-b087-45ed9bad2407
 # ╠═03840394-3a5b-4c24-8b52-15f7e400f900
 # ╠═11c71de9-caa9-40c6-84cb-a0f29d873805
 # ╠═edfc5600-9a4a-4657-b165-8eb3e8540edf
+# ╟─47e7a144-44c0-4770-8f82-1292b0aad8bc
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src/graph_polynomials.jl

@@ -3,7 +3,7 @@ using OMEinsum: NestedEinsum, getixs, getiy
 using FFTW
 using LightGraphs
 
-export contractx, contractf, graph_polynomial, optimize_code
+export contractx, contractf, graph_polynomial
 
 """
     graph_polynomial(problem, method; usecuda=false, kwargs...)
@@ -103,15 +103,26 @@ end
 ############### Problem specific implementations ################
 ### independent set ###
 function generate_tensors(fx, gp::Independence)
-    ixs = getixs(flatten(gp.code))
+    flatten_code = flatten(gp.code)
+    ixs = getixs(flatten_code)
+    n = length(labels(flatten_code))
     T = typeof(fx(ixs[1][1]))
-    return map(ixs) do ix
-        # if the tensor rank is 1, create a vertex tensor.
-        # otherwise the tensor rank must be 2, create a bond tensor.
-        length(ix)==1 ? misv(fx(ix[1])) : misb(T)
+    return Tuple(map(enumerate(ixs)) do (i, ix)
+        if i <= n
+            misv(fx(ix[1]))
+        else
+            misb(T, length(ix)) # if n!=2, it corresponds to set packing problem.
+        end
+    end)
+end
+function misb(::Type{T}, n::Integer=2) where T
+    res = zeros(T, fill(2, n)...)
+    res[1] = one(T)
+    for i=1:n
+        res[1+1<<(i-1)] = one(T)
     end
+    return res
 end
-misb(::Type{T}) where T = [one(T) one(T); one(T) zero(T)]
 misv(val::T) where T = [one(T), val]
 
 graph_polynomial_maxorder(gp::Independence; usecuda) = Int(sum(contractx(gp, TropicalF64(1.0); usecuda=usecuda)).n)

src/networks.jl

@@ -1,4 +1,4 @@
-export Independence, MaximalIndependence, Matching, Coloring
+export Independence, MaximalIndependence, Matching, Coloring, optimize_code, set_packing
 const EinTypes = Union{EinCode,NestedEinsum}
 
 abstract type GraphProblem end
@@ -114,4 +114,27 @@ OMEinsum.timespace_complexity(gp::GraphProblem) = timespace_complexity(gp.code,
 for T in [:Independence, :Matching, :MaximalIndependence]
     @eval bondsize(gp::$T) = 2
 end
-bondsize(gp::Coloring{K}) where K = K
+bondsize(gp::Coloring{K}) where K = K
+
+"""
+    set_packing(sets; kwargs...)
+
+Set packing is a generalization of independent set problem to hypergraphs.
+Calling this function will return you an `Independence` instance.
+`sets` are a vector of vectors, each element being a vertex in the independent set problem. `kwargs` are code optimization parameters.
+
+### Example
+```julia
+julia> sets = [[1, 2, 5], [1, 3], [2, 4], [3, 6], [2, 3, 6]];  # each set is a vertex
+
+julia> gp = set_packing(sets; optmethod=:auto);
+
+julia> res = optimalsolutions(gp; all=true)[]
+(2, {10010, 00110, 01100})ₜ
+```
+"""
+function set_packing(sets; kwargs...)
+    n = length(sets)
+    code = EinCode(([(i,) for i=1:n]..., [(i,j) for i=1:n,j=1:n if j>i && !isempty(sets[i] ∩ sets[j])]...), ())
+    Independence(optimize_code(code; kwargs...))
+end

test/configurations.jl

@@ -42,4 +42,14 @@ end
         @test res5.n == res0
         @test res5.c.data ∈ res2.c.data
     end
+end
+
+@testset "set packing" begin
+    sets = [[1, 2, 5], [1, 3], [2, 4], [3, 6], [2, 3, 6]]  # each set is a vertex
+    gp = set_packing(sets; optmethod=:auto)
+    res = optimalsolutions(gp; all=true)[]
+    @test res.n == 2
+    @test BitVector(Bool[0,0,1,1,0]) ∈ res.c.data
+    @test BitVector(Bool[1,0,0,1,0]) ∈ res.c.data
+    @test BitVector(Bool[0,1,1,0,0]) ∈ res.c.data
 end