Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.
Concept
With high probability
Summary
In mathematics, an event that occurs with high probability (often shortened to w.h.p. or WHP) is one whose probability depends on a certain number n and goes to 1 as n goes to infinity, i.e. the probability of the event occurring can be made as close to 1 as desired by making n big enough.
The term WHP is especially used in computer science, in the analysis of probabilistic algorithms. For example, consider a certain probabilistic algorithm on a graph with n nodes. If the probability that the algorithm returns the correct answer is , then when the number of nodes is very large, the algorithm is correct with a probability that is very near 1. This fact is expressed shortly by saying that the algorithm is correct WHP.
Some examples where this term is used are:
Miller–Rabin primality test: a probabilistic algorithm for testing whether a given number n is prime or composite. If n is composite, the test will detect n as composite WHP. There is a small chance that we are unlucky and the test will think that n is prime. But, the probability of error can be reduced indefinitely by running the test many times with different randomizations.
Freivalds' algorithm: a randomized algorithm for verifying matrix multiplication. It runs faster than deterministic algorithms WHP.
Treap: a randomized binary search tree. Its height is logarithmic WHP. Fusion tree is a related data structure.
Online codes: randomized codes which allow the user to recover the original message WHP.
BQP: a complexity class of problems for which there are polynomial-time quantum algorithms which are correct WHP.
Probably approximately correct learning: A process for machine-learning in which the learned function has low generalization-error WHP.
Gossip protocols: a communication protocol used in distributed systems to reliably deliver messages to the whole cluster using a constant amount of network resources on each node and ensuring no single point of failure.
Official source
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.