Abstract
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 O(n 2 / max{\(\frac{w}{lg^2 w}, \frac{lg^2 n}{(lg lg n)^2}\)}). In the circuit RAM with one nonstandard AC 0 operation, we obtain O(n 2 /\(\frac{w}{lg^2 w}\)). In external memory, we achieve O(n 2 / (MB)), even under the standard assumption of data indivisibility. Cache-obliviously, we obtain a running time of O(n 2 / \(\frac{MB}{lg^2 M}\)). 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.
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Baran, I., Demaine, E.D., Pǎtraşcu, M. (2005). Subquadratic Algorithms for 3SUM. In: Dehne, F., López-Ortiz, A., Sack, JR. (eds) Algorithms and Data Structures. WADS 2005. Lecture Notes in Computer Science, vol 3608. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11534273_36
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DOI: https://doi.org/10.1007/11534273_36
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