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Average-case
In computer science, best, worst, and average cases of a given algorithm express what the Resource (computer science), resource usage is ''at least'', ''at most'' and ''on average'', respectively. Usually the resource being considered is running time, i.e. time complexity, but could also be memory or some other resource. Best case is the function which performs the minimum number of steps on input data of n elements. Worst case is the function which performs the maximum number of steps on input data of size n. Average case is the function which performs an average number of steps on input data of n elements. In real-time computing, the worst-case execution time is often of particular concern since it is important to know how much time might be needed ''in the worst case'' to guarantee that the algorithm will always finish on time. average-case complexity, Average performance and worst-case complexity, worst-case performance are the most used in algorithm analysis. Less widely fou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Average-case Complexity
In computational complexity theory, the average-case complexity of an algorithm is the amount of some computational resource (typically time) used by the algorithm, averaged over all possible inputs. It is frequently contrasted with worst-case complexity which considers the maximal complexity of the algorithm over all possible inputs. There are three primary motivations for studying average-case complexity.O. Goldreich and S. Vadhan, Special issue on worst-case versus average-case complexity, Comput. Complex. 16, 325–330, 2007. First, although some problems may be intractable in the worst-case, the inputs which elicit this behavior may rarely occur in practice, so the average-case complexity may be a more accurate measure of an algorithm's performance. Second, average-case complexity analysis provides tools and techniques to generate hard instances of problems which can be utilized in areas such as cryptography and derandomization. Third, average-case complexity allows discrimina ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Best-case Performance
In computer science, best, worst, and average cases of a given algorithm express what the resource usage is ''at least'', ''at most'' and ''on average'', respectively. Usually the resource being considered is running time, i.e. time complexity, but could also be memory or some other resource. Best case is the function which performs the minimum number of steps on input data of n elements. Worst case is the function which performs the maximum number of steps on input data of size n. Average case is the function which performs an average number of steps on input data of n elements. In real-time computing, the worst-case execution time is often of particular concern since it is important to know how much time might be needed ''in the worst case'' to guarantee that the algorithm will always finish on time. Average performance and worst-case performance are the most used in algorithm analysis. Less widely found is best-case performance, but it does have uses: for example, where the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Smoothed Analysis
In theoretical computer science, smoothed analysis is a way of measuring the complexity of an algorithm. Since its introduction in 2001, smoothed analysis has been used as a basis for considerable research, for problems ranging from mathematical programming, numerical analysis, machine learning, and data mining. It can give a more realistic analysis of the practical performance (e.g., running time, success rate, approximation quality) of the algorithm compared to analysis that uses worst-case or average-case scenarios. Smoothed analysis is a hybrid of worst-case and average-case analyses that inherits advantages of both. It measures the expected performance of algorithms under slight random perturbations of worst-case inputs. If the smoothed complexity of an algorithm is low, then it is unlikely that the algorithm will take a long time to solve practical instances whose data are subject to slight noises and imprecisions. Smoothed complexity results are strong probabilistic r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Amortized Analysis
In computer science, amortized analysis is a method for analyzing a given algorithm's complexity, or how much of a resource, especially time or memory, it takes to execute. The motivation for amortized analysis is that looking at the worst-case run time can be too pessimistic. Instead, amortized analysis averages the running times of operations in a sequence over that sequence. As a conclusion: "Amortized analysis is a useful tool that complements other techniques such as worst-case and average-case analysis." For a given operation of an algorithm, certain situations (e.g., input parametrizations or data structure contents) may imply a significant cost in resources, whereas other situations may not be as costly. The amortized analysis considers both the costly and less costly operations together over the whole sequence of operations. This may include accounting for different types of input, length of the input, and other factors that affect its performance. History Amortize ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time Complexity
In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a fixed amount of time to perform. Thus, the amount of time taken and the number of elementary operations performed by the algorithm are taken to be related by a constant factor. Since an algorithm's running time may vary among different inputs of the same size, one commonly considers the worst-case time complexity, which is the maximum amount of time required for inputs of a given size. Less common, and usually specified explicitly, is the average-case complexity, which is the average of the time taken on inputs of a given size (this makes sense because there are only a finite number of possible inputs of a given size). In both cases, the time complexity is generally express ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Worst-case Execution Time
The worst-case execution time (WCET) of a computational task is the maximum length of time the task could take to execute on a specific hardware platform. What it is used for Worst case execution time is typically used in reliable real-time systems, where understanding the worst case timing behaviour of software is important for reliability or correct functional behaviour. As an example, a computer system that controls the behaviour of an engine in a vehicle might need to respond to inputs within a specific amount of time. One component that makes up the response time is the time spent executing the software – hence if the software worst case execution time can be determined, then the designer of the system can use this with other techniques such as schedulability analysis to ensure that the system responds fast enough. While WCET is potentially applicable to many real-time systems, in practice an assurance of WCET is mainly used by real-time systems that are related to hi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Worst-case Complexity
In computer science (specifically computational complexity theory), the worst-case complexity measures the resources (e.g. running time, memory) that an algorithm requires given an input of arbitrary size (commonly denoted as in asymptotic notation). It gives an upper bound on the resources required by the algorithm. In the case of running time, the worst-case time complexity indicates the longest running time performed by an algorithm given ''any'' input of size , and thus guarantees that the algorithm will finish in the indicated period of time. 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. Definition Given a model of computation and an algorithm \mathsf that halts on each input s, the mapping t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Self-reducibility
Random self-reducibility (RSR) is the rule that a good algorithm for the average case implies a good algorithm for the worst case. RSR is the ability to solve all instances of a problem by solving a large fraction of the instances. Definition If for a function ''f'' evaluating any instance ''x'' can be reduced in polynomial time to the evaluation of ''f'' on one or more random instances ''yi'', then it is self-reducible (this is also known as a ''non-adaptive uniform self-reduction''). In a random self-reduction, an arbitrary worst-case instance ''x'' in the domain of ''f'' is mapped to a random set of instances ''y''1, ..., ''yk''. This is done so that ''f''(''x'') can be computed in polynomial time, given the coin-toss sequence from the mapping, ''x'', and ''f''(''y''1), ..., ''f''(''yk''). Therefore, taking the average with respect to the induced distribution on ''yi'', the average-case complexity of ''f'' is the same (within polynomial factors) as the worst-case randomized ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (including the design and implementation of hardware and software). Computer science is generally considered an area of academic research and distinct from computer programming. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing security vulnerabilities. Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of repositories ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
