TL-HFD extends hyper-flow diffusion with thresholded local updates that are proven exact on the active region, finite-time dual suboptimality bounds, and an activated-volume guarantee, often matching global HFD while scanning less volume on noisy data.
arXiv preprint arXiv:2507.10570 , year=
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Quantum algorithms for triangle listing achieve time Õ(min(n^{5/4}t^{7/12} + n^{7/6}t^{7/9}, m + m^{3/4}t^{1/2}, n^{3/2}t^{1/2})) and enable ε-triangle cut sparsifiers of size Õ(n/ε²) in time Õ(T_q-list + √(mn)/ε).
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Thresholded Local Hyper-Flow Diffusion
TL-HFD extends hyper-flow diffusion with thresholded local updates that are proven exact on the active region, finite-time dual suboptimality bounds, and an activated-volume guarantee, often matching global HFD while scanning less volume on noisy data.
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Quantum Algorithms for Triangle Cut Sparsification
Quantum algorithms for triangle listing achieve time Õ(min(n^{5/4}t^{7/12} + n^{7/6}t^{7/9}, m + m^{3/4}t^{1/2}, n^{3/2}t^{1/2})) and enable ε-triangle cut sparsifiers of size Õ(n/ε²) in time Õ(T_q-list + √(mn)/ε).