Implement functions related to clique decomposition
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Mô tả
Currently, the implementation of clique decomposition computation and `SparseSDPOPF` formulation rely on functions from `PowerModels.jl`. Specifically,
https://github.com/AI4OPT/PGLearn.jl/blob/f07775fee605a0e0852ef00c6d58751a3e6ed767/src/opf/opf.jl#L287-L295
https://github.com/AI4OPT/PGLearn.jl/blob/f07775fee605a0e0852ef00c6d58751a3e6ed767/src/opf/sparse_sdpwrm.jl#L383-L412
- Regarding clique decomposition computation, `PowerModels.jl` computes chordal extension using the Cholesky decomposition (https://github.com/lanl-ansi/PowerModels.jl/blob/be6af59202a6868b20a41214cb341b883d62e5f0/src/form/wrm.jl#L321). This can, for example, be replaced with calls to functions in [CliqueTrees.jl](https://github.com/AlgebraicJulia/CliqueTrees.jl), a package specifically for computing chordal extension.
- Regarding `SparseSDPOPF` formulation: utility functions from `PowerModels.jl` are being used to compute pairs of cliques with overlapping nodes and indices of identical elements in two arrays. The implementation of these utility functions is not complicated and can probably be taken without making much modification.
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