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Worst-case performance analysis and average-case performance analysis have some similarities, but in practice usually require different tools and approaches. Determining what typical input means is difficult, and often that average input has properties which make it difficult to characterise mathematically (consider, for instance, algorithms ...
A worst case effect needs only to be seen once during testing for the analysis to be able to combine it with other worst case events in its analysis. Typically, the small sections of software can be measured automatically using techniques such as instrumentation (adding markers to the software) or with hardware support such as debuggers, and ...
Big O notation is a convenient way to express the worst-case scenario for a given algorithm, although it can also be used to express the average-case — for example, the worst-case scenario for quicksort is O(n 2), but the average-case run-time is O(n log n).
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Worst-case complexity: This is the complexity of solving the problem for the worst input of size . The order from cheap to costly is: Best, average (of discrete uniform distribution), amortized, worst. For example, the deterministic sorting algorithm quicksort addresses the problem of sorting a list of integers. The worst-case is when the pivot ...
For example, a triangular distribution might be used, depending on the application. In three-point estimation, three figures are produced initially for every distribution that is required, based on prior experience or best-guesses: a = the best-case estimate; m = the most likely estimate; b = the worst-case estimate
Because software, unlike a major civil engineering construction project, is often easy and cheap to change after it has been constructed, a piece of custom software that fails to deliver on its objectives may sometimes be modified over time in such a way that it later succeeds—and/or business processes or end-user mindsets may change to accommodate the software.
In this case, Yao's principle describes an equality between the average-case complexity of deterministic communication protocols, on an input distribution that is the worst case for the problem, and the expected communication complexity of randomized protocols on their worst-case inputs. [6] [14] An example described by Avi Wigderson (based on ...