We give a randomized polynomial-time algorithm that, for every fixed $\varepsilon>0$, colors every $3$-colorable $n$-vertex graph using $O\bigl(n^{(13-\sqrt{97})/18+\varepsilon}\bigr) \approx O\bigl(n^{0.17506+\varepsilon}\bigr)$ colors, improving upon the previous best bound of $O(n^{0.19539})$ from Bansal, Huang, and...
We study deterministic approximation algorithms for the permanent of a nonnegative matrix through the Bethe permanent, an approximation computable in polynomial time. The tight analysis of Anari and Rezaei gives a universal comparison between the permanent and the Bethe permanent within a factor $(\sqrt 2)^n$. The simp...
The worst-case tractability of approximate counting and sampling of fixed-size slices for bipartite independent set problems for bipartite independent set problems is studied.
Ijay Narang, Will Perkins, Yu-Zhou Wang et al.· 1 citation
Beyond strong convexity, for general convex SGD, a Gibbs limiting law is identified and a pre-limit Wasserstein approximation error under stability and Stein-equation hypothesis is proved, which are validated numerically.
Zedong Wang, Yu-Yang Wang, Ijay Narang et al.· 1 citation
The main idea is to introduce a family of quadratic tilts in the left-right occupation imbalance and show that each tilted measure can be sampled efficiently using Glauber dynamics, and obtain efficient approximate counting and sampling at every fugacity $\lambda>0$ whenever.
Ijay Narang, Will Perkins· 0 citations
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