Green's conjecture and testing linear-invariant properties
Proceedings of the forty-first annual ACM symposium on Theory of computing
Finding, minimizing, and counting weighted subgraphs
Proceedings of the forty-first annual ACM symposium on Theory of computing
Approximate Matching for Run-Length Encoded Strings Is 3sum-Hard
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
A (slightly) faster algorithm for Klee's measure problem
Computational Geometry: Theory and Applications
Towards polynomial lower bounds for dynamic problems
Proceedings of the forty-second ACM symposium on Theory of computing
Exact weight subgraphs and the k-sum conjecture
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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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 AC0 operation, we obtain $O(n^{2}/\frac{w^{2}}{\lg^{2}w})$. In external memory, we achieve O(n2/(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.