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Preprint Aug 2026

Faster Minimum k-Cut I: Simple and Sparse Weighted Graphs

The minimum $k$-cut problem asks for the fewest edges whose removal leaves an input graph with at least $k$ connected components. Previously, the best algorithm for simple graphs ran in $O_k(n^{(1-\varepsilon)k+O(1)})$ time~\cite{HL22}, showing that the \(n^k\) barrier can be broken up to a polynomial overhead. We give...

Jason Li, Trevor Vaughn · 0 citations
Preprint Aug 2026

Deterministic Spectral Sparsification in Almost-Linear Time for Dense Graphs

Deterministic expander decomposition, along with replacing vertices by fixed expander graphs to achieve approximate regularity, extends these algorithms to general graphs and evaluates the resulting conditional-expectation scores in two ways.

Jason Li, Trevor Vaughn · 0 citations

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