Fast implementation of triangulation algorithms.

[samuelsonric]

I have a package CliqueTrees.jl with fast implementations of various graph triangulation algorithms. Here are some benchmarks.

julia> using Graphs, MatrixMarket, SuiteSparseMatrixCollection, SparseArrays, TSSOS

julia> ssmc = ssmc_db();

julia> name = "bcsstk11";

julia> matrix = mmread(joinpath(fetch_ssmc(ssmc[ssmc.name .== name, :], format="MM")[1], "$(name).mtx"));

julia> graph = Graph(fkeep!((i, j, x) -> i != j, matrix))
{1473, 16384} undirected simple Int64 graph

old implementation

julia> @time TSSOS.chordal_cliques!(copy(graph); method="MF", minimize=false);
  7.749093 seconds (96.07 k allocations: 67.437 MiB, 0.27% gc time)

julia> @time TSSOS.chordal_cliques!(copy(graph); method="MF", minimize=true);
  9.379268 seconds (311.25 k allocations: 142.738 MiB, 0.12% gc time)

new implementation

julia> @time TSSOS.chordal_cliques!(copy(graph); method="MF", minimize=false);
  0.011180 seconds (14.00 k allocations: 6.338 MiB)

julia> @time TSSOS.chordal_cliques!(copy(graph); method="MF", minimize=true);
  0.042636 seconds (22.98 k allocations: 11.396 MiB)

[samuelsonric]

Here, I am benchmarking the Broyden banded function from example 7.1 of this paper.

julia> using DynamicPolynomials, TSSOS

julia> function broyden_banded(n)
           @polyvar x[1:n]
    
           g = sum(1:n) do i
               f = x[i] * (2 + 5x[i]^2) + 1
        
               for j in max(1, i - 5):min(n, i + 1)
                   if i != j
                       f += (1 + x[j]) * x[j]
                   end
               end
        
               return f^2
           end
    
           return g, x
       end;

julia> f, x = broyden_banded(500);

old implementation

julia> @time cs_tssos_first([f], x, 3; TS="MF");
 91.944828 seconds (5.83 G allocations: 219.252 GiB, 22.71% gc time)

new implementation

julia> @time cs_tssos_first([f], x, 3; TS="MF");
 78.821616 seconds (5.37 G allocations: 201.896 GiB, 23.82% gc time)

[wangjie212]

Thank you very much for introducing this nice package to me!

[samuelsonric]

Let me know if there are any problems.

[mschauer]

@samuelsonric on a run mschauer/CausalInference.jl#168 👍