An efficient formula for linear recurrences
SIAM Journal on Computing
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Division by invariant integers using multiplication
PLDI '94 Proceedings of the ACM SIGPLAN 1994 conference on Programming language design and implementation
On a class of O(n2) problems in computational geometry
Computational Geometry: Theory and Applications
Algorithmic number theory
A sublinear additive sieve for finding prime number
Communications of the ACM
On the Power of Random Access Machines
Proceedings of the 6th Colloquium, on Automata, Languages and Programming
On the Ultimate Complexity of Factorials
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Capabilities and Complexity of Computations with Integer Division
STACS '93 Proceedings of the 10th Annual Symposium on Theoretical Aspects of Computer Science
A characterization of the power of vector machines
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
Deterministic sorting in O(nlog logn) time and linear space
Journal of Algorithms
Valiant's model and the cost of computing integers
Computational Complexity
On the Complexity of Numerical Analysis
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
The complexity of approximating the square root
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Algebraic Complexity Theory
Subquadratic algorithms for 3SUM
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
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The unit cost model is both convenient and largely realistic for describing integer decision algorithms over + ,×. Additional operations like division with remainder or bitwise conjunction, although equally supported by computing hardware, may lead to a considerable drop in complexity. We show a variety of concrete problems to benefit from such non-arithmetic primitives by presenting and analyzing corresponding fast algorithms.