Worst-case Subset Sum in time 2^((1/2 - c)n)

Theorem 1.1: a uniform randomized word-RAM algorithm decides Subset Sum with error at most 1/3 on every input and runs in worst-case time $O(2^{0.49n})$ for every fixed polynomial bound on input bit length, the time bound holding on every random execution. The method combines isolation, a random prime modulus, a filtered Fourier checksum and alias extraction. It is not deterministic, it does not treat super-polynomial bit lengths, and it does not improve the space bound. The companion manuscript separately gives one-sided error, time $\mathrm{poly}(n)2^{n/2}$ and space $O(2^{n/5})$.

Theorem 1.1: a uniform randomized word-RAM algorithm decides Subset Sum with error at most 1/3 on every input and runs in worst-case time $O(2^{0.49n})$ for every fixed polynomial bound on input bit length, the time bound holding on every random execution. The method combines isolation, a random prime modulus, a filtered Fourier checksum and alias extraction. It is not deterministic, it does not treat super-polynomial bit lengths, and it does not improve the space bound. The companion manuscript separately gives one-sided error, time $\mathrm{poly}(n)2^{n/2}$ and space $O(2^{n/5})$.