Shafi Goldwasser, Dhiraj Holden

We set out to study the impact of having access to correlated instances on the fine grained complexity of polynomial time problems, which have notoriously resisted improvement.

In particular, we show how to use a logarithmic number of auxiliary correlated instances to obtain $o(n^2)$ time algorithms for the longest common ...
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Venkatesan Guruswami, Xiaoyu He, Ray Li

We prove that there exists an absolute constant $\delta>0$ such any binary code $C\subset\{0,1\}^N$ tolerating $(1/2-\delta)N$ adversarial deletions must satisfy $|C|\le 2^{\poly\log N}$ and thus have rate asymptotically approaching $0$. This is the first constant fraction improvement over the trivial bound that codes tolerating $N/2$ adversarial deletions must have rate ... more >>>