Asymptotic Analysis of Algorithms

This text discusses the asymptotic analysis of algorithms, using the big-Omega and little-omega symbols.

The big-Omega symbol is used to denote lower bounds on the running time of an algorithm, while the little-omega symbol is used to denote upper bounds.

The text also provides examples of how to use these symbols.

Questions

• What is the difference between big-Omega and little-omega?
• How are these symbols used to denote lower and upper bounds on the running time of an algorithm?
• What are some examples of how to use these symbols?

Answers

• The big-Omega symbol is used to denote lower bounds on the running time of an algorithm, while the little-omega symbol is used to denote upper bounds.
• These symbols are used by comparing the running time of an algorithm to a function f. If the running time of the algorithm is at least f, then we say that the algorithm is Omega(f). If the running time of the algorithm is at most f, then we say that the algorithm is little-omega(f).
• Some examples of how to use these symbols include:
  * x^2 is Omega(x)
  * 2x is Omega(x^2)
  * x/100 is Omega(100x + px)

The little-omega symbol is not as widely used as the other asymptotic symbols we defined.