Improved parallel integer sorting without concurrent writing
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
On a class of O(n2) problems in computational geometry
Computational Geometry: Theory and Applications
Fusion trees can be implemented with AC0 instructions only
Theoretical Computer Science
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Introduction to Algorithms
Universal Hashing and k-Wise Independent Random Variables via Integer Arithmetic without Primes
STACS '96 Proceedings of the 13th Annual Symposium on Theoretical Aspects of Computer Science
Static Dictionaries on RAMs: Query Time is Necessary and Sufficient
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Scalable computation of acyclic joins
Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Graphical Models - Special issue on PG2004
Fast algorithms for finding disjoint subsequences with extremal densities
Pattern Recognition
Necklaces, convolutions, and X + Y
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
A (slightly) faster algorithm for klee's measure problem
Proceedings of the twenty-fourth annual symposium on Computational geometry
On Faster Integer Calculations Using Non-arithmetic Primitives
UC '08 Proceedings of the 7th international conference on Unconventional Computing
Fast algorithms for finding disjoint subsequences with extremal densities
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
| Hi-index | 0.00 |
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(n2 / 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(n2 /$\frac{w}{lg^2 w}$). 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(n2 / $\frac{MB}{lg^2 M}$). 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.