Is There a Difference Between Average Case Complexity and Expected Running Time?

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SUMMARY

The discussion clarifies the distinction between average case complexity and expected running time in algorithms. Average case complexity applies to deterministic algorithms, exemplified by quicksort, representing the expected runtime when inputs are randomly selected. In contrast, expected running time pertains to randomized algorithms, such as Karger's algorithm, indicating the expected runtime for specific inputs. Additionally, the concept of expected worst case running time is introduced, referring to the worst case of expected running time across all inputs of a given size.

PREREQUISITES
  • Understanding of algorithmic complexity, specifically average case complexity
  • Familiarity with deterministic algorithms, particularly quicksort
  • Knowledge of randomized algorithms, such as Karger's algorithm
  • Concept of expected value in probability and statistics
NEXT STEPS
  • Research the average case complexity of various sorting algorithms
  • Explore the implementation and analysis of Karger's algorithm
  • Study the concept of expected worst case running time in randomized algorithms
  • Learn about the implications of input distribution on algorithm performance
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Students and professionals in computer science, particularly those studying algorithms, data structures, and performance analysis of both deterministic and randomized algorithms.

naftali
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Hi,

I am not sure if I understand well : is there a difference between avarage case complexity to expectation of running time?

thank you

Naftali
 
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Well, different authors might use them in different ways, but here's how I learned it...
"Average case" running time is for a deterministic algorithm (the most familiar example that you use average case runtime for is quicksort). It is the expected value of the running time that the algorithm would have if inputs were chosen randomly.

"Expected" running time is usually for a randomized algorithm (for example, Karger's algorithm). It is the expected value for the runtime of the algorithm on a particular input. You might also speak of expected worst case running time, which would be the worst case of the expected running time over all inputs of a certain size.
 
Thanks
 

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