Author

Dmitriy Kunisky

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Preprint Sep 2026

Improved polynomial-time algorithms for detecting and recovering planted $\Theta(\sqrt{n})$-cliques

In the planted clique problem, one observes either an Erd\H{o}s--R\'{e}nyi graph on $n$ vertices or such a graph with a clique added to $k = k(n)$ vertices, and seeks to detect or recover the clique. It is widely believed that $k = \Theta(\sqrt{n})$ is the smallest clique size for which polynomial-time algorithms exist...

Dmitriy Kunisky, Song-Tao Mao · 0 citations

Preprint Aug 2026

Inequalities for rank-two permanents and finite free convolutions

Bang (1976) proved the inequality for matrix permanents $\mathrm{per}^2(A) \geq 2^{-2n}\mathrm{per}(A \otimes J_2)$, where $J_2$ is the $2 \times 2$ all-ones matrix and $A$ is any $n \times n$ matrix with non-negative entries. We show that, if $A$ is any $n \times n$ real-valued matrix with rank at most two (possibly h...

Dmitriy Kunisky, D. Spielman, Xi-Fan Yu · 0 citations