The streaming and read-only algorithms presented in the paper exhibit trade-offs between space, time, and error probability. Here are some fundamental limitations and trade-offs:
Space Complexity: The streaming algorithms require less space compared to the read-only algorithms but may sacrifice accuracy due to the probabilistic nature of the computations. The trade-off lies in balancing space efficiency with error probability.
Time Complexity: The read-only algorithms may have higher time complexity per character compared to streaming algorithms, especially in the worst-case scenarios. This trade-off between time and space efficiency needs to be considered based on the specific requirements of the application.
Error Probability: The streaming algorithms have an error probability that is inverse-polynomial in the input size, which can impact the accuracy of the results. The trade-off here is between achieving faster computations with a certain level of error tolerance.
Scalability: As the input size increases, the algorithms may face scalability challenges in terms of memory usage and processing time. Balancing scalability with efficiency is crucial in real-world applications.
Complexity vs. Accuracy: There is a trade-off between the complexity of the algorithms and the accuracy of the results. More complex algorithms may provide more accurate distance computations but at the cost of increased computational resources.