On query result integrity over encrypted data by Esiner, Ertem, Datta, Anwitaman

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Computing permanents and counting Hamiltonian cycles by listing dissimilar vectors by Williams, Richard Ryan, Björklund, Andreas

“…This improves on a Las Vegas algorithm running in expected 2n−Ω(n/(r log r)) time, implicit in [Björklund, Husfeldt, and Lyckberg, IPL 2017]. For the permanent over the integers of a 0/1-matrix with exactly d ones per row and column, we provide a deterministic 2n−Ω(d3 n /4) time algorithm. …”
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Improved Merlin–Arthur Protocols for Central Problems in Fine-Grained Complexity by Akmal, Shyan, Chen, Lijie, Jin, Ce, Raj, Malvika, Williams, Ryan

“…For example, our work implies that certifying there is no Subset Sum solution to n integers can be done in Merlin–Arthur time $$2^{n/3}\cdot \textrm{poly}(n)$$ 2 n / 3 · poly ( n ) , improving on the previous best protocol by Nederlof [IPL 2017] which took $$2^{0.49991n}\cdot \textrm{poly}(n)$$ 2 0.49991 n · poly ( n ) time.…”
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