Sumsets, 3SUM, Subset Sum: Now for Real!
Nick Fischer · Society for Industrial and Applied Mathematics eBooks · 2025
We study a broad class of algorithmic problems with an “additive flavor” such as computing sumsets, 3SUM, Subset Sum and geometric pattern matching. Our starting point is that these problems can often be solved efficiently for integers, owed to the rich available tool set including bit-tricks, linear hashing, and the Fast Fourier Transform. However, for real numbers these tools are not available, leading to significant gaps in the best-known running times for integer inputs versus for real inputs. In this work our goal is to close this gap.