Suppose $T_1$ and $T_2$ represent two Laplacian matrices of two spanning trees of $n$ vertices. Since the Cholesky factorization needs $O(n)$ time for each $T_i\ (i=1,2)$ due to the tree structure, the question is: Is there any way to factorize, e.g., using Cholesky factorization, the matrix $T:=T_1-T_2$ in $\widetilde{O}(n)$ time? What is the upper bound of time to factorize the matrix $T$?
2026-03-25 17:38:24.1774460304
Fast Cholesky Factrorization for Tree Laplacians
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