Analysis of randomized algorithms
To analyze randomized algorithms, we often use probabilistic analysis. Instead of focusing on the worst-case scenario, we examine the expected performance of the algorithm over all possible random choices. This expected value provides a more realistic picture of the algorithm’s typical behavior. Here are the key principles:
- We calculate the expected value of key performance metrics, such as running time or space usage. This involves averaging the performance over all possible inputs, weighted by their probability.
- We study the distribution and variance of the algorithm’s performance metrics to understand how much they deviate from the expected value. This helps in assessing the reliability and consistency of the algorithm.
- The focus is on analyzing the algorithm’s behavior on typical or randomly chosen inputs rather than worst-case inputs. This provides a more realistic measure of the algorithm’s practical...
