Baran, I., Demaine, E.D. & Pǎtraşcu, M. Algorithmica (2008) 50: 584. doi:10.1007/s00453-007-9036-3
We obtain subquadratic algorithms for 3SUM on integers and rationals in several models. On a standard word RAM with w-bit words, we obtain a running time of
. In the circuit RAM with one nonstandard AC0 operation, we obtain
. In external memory, we achieve O(n2/(MB)), even under the standard assumption of data indivisibility. Cache-obliviously, we obtain a running time of
. In all cases, our speedup is almost quadratic in the “parallelism” the model can afford, which may be the best possible. Our algorithms are Las Vegas randomized; time bounds hold in expectation, and in most cases, with high probability.