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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).
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 ...
Analysis of algorithms—how to determine the resources needed by an algorithm; Benchmark—a method for measuring comparative execution times in defined cases; Best, worst and average case—considerations for estimating execution times in three scenarios; Compiler optimization—compiler-derived optimization; Computational complexity theory
The order of growth (e.g. linear, logarithmic) of the worst-case complexity is commonly used to compare the efficiency of two algorithms. The worst-case complexity of an algorithm should be contrasted with its average-case complexity, which is an average measure of the amount of resources the algorithm uses on a random input.
b = the worst-case estimate These are then combined to yield either a full probability distribution, for later combination with distributions obtained similarly for other variables, or summary descriptors of the distribution, such as the mean , standard deviation or percentage points of the distribution.
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]