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Finding Cheeger Cuts in Hypergraphs via Heat Equation
Masahiro Ikeda, Atsushi Miyauchi, Yuuki Takai +1
Cheeger's inequality states that a tightly connected subset can be extracted from a graph using an eigenvector of the normalized Laplacian associated with . More specificall…
Spectral Sparsification of Hypergraphs
Tasuku Soma, Yuichi Yoshida
For an undirected/directed hypergraph , its Laplacian is defined such that its ``quadratic form'' $\boldsymbol{x}^\top L_G(\boldsym…
Sublinear-Time Quadratic Minimization via Spectral Decomposition of Matrices
Amit Levi, Yuichi Yoshida
We design a sublinear-time approximation algorithm for quadratic function minimization problems with a better error bound than the previous algorithm by Hayashi and Yoshida (NIPS'1…
Polynomial-Time Algorithms for Submodular Laplacian Systems
Kaito Fujii, Tasuku Soma, Yuichi Yoshida
Let be an undirected graph, be the associated Laplacian matrix, and be a vector. Solving the Laplacian system $L_G x…