How Randomness Improves Algorithms?
10 days ago
- #computer-science
- #randomized-algorithms
- #primality-testing
- Randomness has been used in computer science since its inception, aiding in simulations for nuclear processes, astrophysics, climate science, and economics.
- Randomized algorithms can efficiently solve unambiguous true-or-false questions, such as primality testing, by leveraging probabilistic methods.
- Fermat's little theorem forms the basis for primality tests using randomness, where multiple trials can confirm a number's primality with high certainty.
- Randomness helps solve problems by reframing them to require only an appropriate random value, even if the ideal value is unknown.
- In 1994, Nisan and Wigderson showed that randomness might not be necessary, suggesting that problems solvable with randomness could also have efficient deterministic solutions.
- De-randomizing randomized algorithms is often challenging, making randomness a practical choice despite theoretical advances.
- A recent breakthrough in graph theory used randomness to simplify pathfinding in graphs with negative segments, proving most random choices are effective.
- Randomness is widely used in cryptography, game theory, and machine learning, demonstrating its enduring importance in computer science.