Polynomial-time algorithms for submodular Laplacian systems
نویسندگان
چکیده
Let G=(V,E) be an undirected graph, LG∈RV×V the associated Laplacian matrix, and b∈RV a vector. Solving system LGx=b has numerous applications in theoretical computer science, machine learning, network analysis. Recently, notion of operator LF:RV→2RV for submodular transformation F:2V→R+E was introduced, which can handle graphs, directed hypergraphs, joint distributions unified manner. In this study, we show that LF(x)∋b solved polynomial time. Furthermore, prove even when no solution, solve its regression form Finally, discuss potential systems learning
منابع مشابه
Polynomial-Time Algorithms for Submodular Laplacian Systems
Let G = (V,E) be an undirected graph, LG ∈ R ×V be the associated Laplacian matrix, and b ∈ R V be a vector. Solving the Laplacian system LGx = b has numerous applications in theoretical computer science, machine learning, and network analysis. Recently, the notion of the Laplacian operator LF : R V → 2 V for a submodular transformation F : 2 → RE+ was introduced, which can handle undirected gr...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2021
ISSN: ['1879-2294', '0304-3975']
DOI: https://doi.org/10.1016/j.tcs.2021.09.019