Implement KaHyPar optimizer

Project.toml

@@ -9,7 +9,9 @@ Combinatorics = "861a8166-3701-5b0c-9a16-15d98fcdc6aa"
 DataStructures = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
 GraphMakie = "1ecd5474-83a3-4783-bb4f-06765db800d2"
 Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6"
+KaHyPar = "2a6221f6-aa48-11e9-3542-2d9e0ef01880"
 Memoize = "c03570c3-d221-55d1-a50c-7939bbd78826"
+SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 
 [weakdeps]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"

src/EinExprs.jl

@@ -13,6 +13,6 @@ export findslices, FlopsScorer, SizeScorer
 
 include("Optimizers/Optimizers.jl")
 export Optimizer, einexpr
-export Exhaustive, Greedy
+export Exhaustive, Greedy, HyPar
 
 end

src/Optimizers/KaHyPar.jl

@@ -0,0 +1,48 @@
+using AbstractTrees
+using SparseArrays
+using KaHyPar
+
+@kwdef struct HyPar <: Optimizer
+    parts = 2
+    imbalance = 0.03
+    cutoff = 2
+    configuration::Union{Nothing,Symbol,String} = nothing
+end
+
+function EinExprs.einexpr(config::HyPar, path)
+    inds = mapreduce(head, ∪, path.args)
+    indexmap = Dict(Iterators.map(splat(Pair) ∘ reverse, enumerate(inds)))
+
+    num_columns = maximum(values(indexmap))
+    num_rows = length(path.args)
+    incidence_matrix = spzeros(Int, num_rows, num_columns)
+
+    # Iterate through each tensor and its associated indices, and update the incidence matrix.
+    for (i, tensor) in enumerate(path.args)
+        tensor_indices = [i]  # Current tensor is represented as a row in the matrix.
+        edge_indices = [indexmap[idx] for idx in head(tensor)]  # Map indices via 'indexmap'.
+
+        # Create a subview for the current tensor and associated hyperedges.
+        incidence_subview = view(incidence_matrix, tensor_indices, edge_indices)
+        incidence_subview .= 1  # Update the subview directly. This step modifies the original sparse matrix.
+    end
+
+    # NOTE indices in `inds` should be in the same order as unique indices appear by iterating on `path.args` because `∪` retains order
+    edge_weights = map(Base.Fix1(size, path), inds)
+    vertex_weights = ones(Int, length(path.args))
+
+    hypergraph = KaHyPar.HyperGraph(incidence_matrix, vertex_weights, edge_weights)
+
+    # stop on cutoff
+    hypergraph.n_vertices <= config.cutoff && return path
+
+    partitions =
+        KaHyPar.partition(hypergraph, config.parts; imbalance = config.imbalance, configuration = config.configuration)
+
+    args = map(unique(partitions)) do partition
+        expr = sum(path.args[partitions.==partition], skip = path.head)
+        einexpr(config, expr)
+    end
+
+    return EinExpr(path.head, args)
+end

src/Optimizers/Optimizers.jl

@@ -8,3 +8,4 @@ einexpr(config::Optimizer, expr) = einexpr(config, expr)
 include("Naive.jl")
 include("Exhaustive.jl")
 include("Greedy.jl")
+include("KaHyPar.jl")

test/KaHyPar_test.jl

@@ -0,0 +1,50 @@
+@testset "KaHyPar" begin
+    @testset begin
+        tensors = [
+            EinExpr([:j, :b, :i, :h], Dict(i => 2 for i in [:j, :b, :i, :h])),
+            EinExpr([:a, :c, :e, :f], Dict(i => 2 for i in [:a, :c, :e, :f])),
+            EinExpr([:j], Dict(i => 2 for i in [:j])),
+            EinExpr([:e, :a, :g], Dict(i => 2 for i in [:e, :a, :g])),
+            EinExpr([:f, :b], Dict(i => 2 for i in [:f, :b])),
+            EinExpr([:i, :h, :d], Dict(i => 2 for i in [:i, :h, :d])),
+            EinExpr([:d, :g, :c], Dict(i => 2 for i in [:d, :g, :c])),
+        ]
+
+        path = einexpr(HyPar, EinExpr(Symbol[], tensors))
+
+        @test path isa EinExpr
+
+        @test mapreduce(flops, +, Branches(path)) == 108
+    end
+
+    @testset begin
+        tensors = [
+            EinExpr([:F, :P, :V], Dict(:P => 5, :F => 8, :V => 5)),
+            EinExpr([:T, :Y, :V, :X, :N, :B], Dict(:T => 5, :N => 2, :B => 5, :V => 5, :Y => 7, :X => 8)),
+            EinExpr([:L, :K, :S], Dict(:K => 8, :L => 7, :S => 5)),
+            EinExpr([:M, :J, :Q, :O], Dict(:M => 5, :J => 7, :Q => 7, :O => 6)),
+            EinExpr([:c], Dict(:c => 2)),
+            EinExpr([:I, :U, :E], Dict(:U => 8, :I => 5, :E => 6)),
+            EinExpr([:N, :C], Dict(:N => 2, :C => 4)),
+            EinExpr([:a, :K], Dict(:a => 3, :K => 8)),
+            EinExpr([:d, :E, :M], Dict(:M => 5, :d => 6, :E => 6)),
+            EinExpr([:B, :b, :D, :H, :L], Dict(:b => 5, :H => 7, :D => 8, :B => 5, :L => 7)),
+            EinExpr([:c, :P, :X, :Q], Dict(:P => 5, :Q => 7, :c => 2, :X => 8)),
+            EinExpr([:G], Dict(:G => 6)),
+            EinExpr([:Z, :W], Dict(:Z => 9, :W => 6)),
+            EinExpr([:Y, :H, :S], Dict(:H => 7, :S => 5, :Y => 7)),
+            EinExpr([:O, :F, :b, :I], Dict(:b => 5, :I => 5, :F => 8, :O => 6)),
+            EinExpr([:A, :J, :T, :G], Dict(:T => 5, :A => 6, :J => 7, :G => 6)),
+            EinExpr([:Z, :D, :R], Dict(:Z => 9, :R => 8, :D => 8)),
+            EinExpr([:R, :U], Dict(:U => 8, :R => 8)),
+            EinExpr([:A, :W], Dict(:A => 6, :W => 6)),
+            EinExpr([:a, :C, :d], Dict(:a => 3, :d => 6, :C => 4)),
+        ]
+
+        path = einexpr(HyPar, EinExpr(Symbol[], tensors))
+
+        @test path isa EinExpr
+
+        @test mapreduce(flops, +, Branches(path)) == 31653164
+    end
+end

test/runtests.jl

@@ -8,6 +8,7 @@ using EinExprs
         include("Naive_test.jl")
         include("Exhaustive_test.jl")
         include("Greedy_test.jl")
+        include("KaHyPar_test.jl")
     end
     include("Slicing_test.jl")
 end