Author

Colin Tang

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Preprint Oct 2026

Faster high-accuracy multicommodity flow in dense graphs

We give a fast algorithm for solving min-cost $k$-commodity flow. The basic idea is to construct an auxiliary linear program that has low rank and whose minimum value is at most $1/k$ times the minimum value of the original problem (thus, solving this auxiliary linear program will make at least $1/k$ fraction of progre...

Chen-Xin Dai, Alicia Stepin, Colin Tang · 0 citations

Preprint Oct 2026

Near-Optimal Oracle Bounds for Isotropic Rounding

We give optimal bounds, up to polylogarithmic factors, for rounding convex bodies to near-isotropic position. A convex body $B(0,r)\subseteq K\subseteq B(0,R)$ in $\R^n$ can be rounded using $\Ot(n^3)$ membership queries; the upper bound extends to logconcave distributions. We prove a matching $\Omegat(n^3)$ lower boun...

Yang P. Liu, Richard Peng, Alicia Stepin et al. · 0 citations