CAST: Canonical Approximate Schur Tree for Approximate Cholesky on Graphs
Graph-data workloads such as diffusion estimation, ranking, semi-supervised learning, and network optimization often solve many Laplacian or symmetric diagonally dominant M-matrix (SDDM) systems with the same coefficient matrix. Approximate Cholesky preconditioners eliminate vertices one at a time and store the resulting sparse approximate factorization, the \emph{factor}, whose construction cost is amortized across these solves. But eliminating a vertex, the \emph{pivot}, creates a dense Schur-complement clique among its $d$ active neighbors. We introduce CAST (Canonical Approximate Schur Tree), which replaces this clique with a weighted random spanning tree sampled directly from it. Eve...
| Authors | Meher Chaitanya, Cameron Musco, Aristides Gionis |
|---|---|
| Primary category | stat.ML |
| Published | 8 September 2026 |
| Last updated at source | 8 September 2026 |
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