The complexity of problems on probabilistic, nondeterministic, and alternating decision trees
Journal of the ACM (JACM)
The effect of number of Hamiltonian paths on the complexity of a vertex-coloring problem
SIAM Journal on Computing
The decision-tree complexity of element distinctness
Information Processing Letters
Randomized algorithms
Probabilistic, nondeterministic, and alternating decision trees (Preliminary Version)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Lower bounds for algebraic computation trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Quantum lower bounds for the collision and the element distinctness problems
Journal of the ACM (JACM)
Quantum Algorithms for Element Distinctness
SIAM Journal on Computing
Probabilistic computations: Toward a unified measure of complexity
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Journal of Computer and System Sciences
Abstract models of computation in cryptography
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
| Hi-index | 0.00 |
We consider the well known problem of finding two identical elements, called a collision, in a list of n numbers. Here, the (very fast) comparison based algorithms are randomized and will only report existing collisions, and do this with (small) probability p, the success probability. We find a trade-off between p and the running time t, and show that this trade-off is optimal up to a constant factor. For worst-case running time t, the optimal success probability is p = Θ(min{t/n, 1}t/(n log t)). For expected running time t, the success probability is p = Θ(t/(n log n)).