Topic
Average-case complexity
About: Average-case complexity is a research topic. Over the lifetime, 1749 publications have been published within this topic receiving 44972 citations.
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01 Jun 2012TL;DR: In this paper, some complexity aspects of incremental algorithm for creation of generalized one-sided concept lattices are provided and it is shown that complexity of presented algorithm asymptotically becomes linear function depending on the number of objects in formal context.
Abstract: In this paper we provide some complexity aspects of incremental algorithm for creation of generalized one-sided concept lattices. The novelty of this algorithm is in its possibility to work with different types of attributes and produce one-sided concept lattice from the generalized one-sided formal context. As it is shown in the paper, the complexity of the algorithm is in general exponential. However, in practice it is reasonable to consider special cases, where the number of attributes is fixed. Then complexity of presented algorithm asymptotically becomes linear function depending on the number of objects in formal context.
8 citations
01 Jan 1989
TL;DR: In this paper, the computational complexity of integrals and derivatives of convex functions defined on the interval was studied. But the complexity of the integrals was not studied. And the derivatives of the derivatives were not considered.
Abstract: In this paper,we study the computational complexity of the integrals and the derivatives of
convex functions defined on the interval [0,1].
8 citations
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TL;DR: In this paper, the authors studied the dependence of the average-case complexity of the k-clique problem on the parameter k and showed that k-Clique admits both analogues for Erd?s-Renyi random graphs of arbitrary density.
8 citations
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TL;DR: In this article, an analysis of the complexity of known solution algorithms for four problems of number theory is given, including the solving of Diophantine equations and inequalities and the seeking of diophantine approximations and solutions of quadratic DDEs.
Abstract: An analysis of the complexity of the known solution algorithms is given for four problems of number theory — the solving of Diophantine equations and inequalities and the seeking of Diophantine approximations and solutions of quadratic Diophantine equations. A comparison is made of the various algorithms on the basis of their time complexity. The relation of time complexity to the sizes of the intermediate numbers is particularly stressed. A machine independent description of complexity classes is given and some open problems are formulated.
8 citations
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15 May 2006TL;DR: In this paper, the authors propose an alternative measure of complexity for approximations-optimization tasks, which is to define a hierarchy on the set of inputs to a learning task, so that natural (real data) inputs occupy only bounded levels of this hierarchy and there are algorithms that handle in polynomial time each such bounded level.
Abstract: We address a fundamental problem of complexity theory – the inadequacy of worst-case complexity for the task of evaluating the computational resources required for real life problems While being the best known measure and enjoying the support of a rich and elegant theory, worst-case complexity seems gives rise to over-pessimistic complexity values Many standard task, that are being carried out routinely in machine learning applications, are NP-hard, that is, infeasible from the worst-case-complexity perspective In this work we offer an alternative measure of complexity for approximations-optimization tasks Our approach is to define a hierarchy on the set of inputs to a learning task, so that natural (’real data’) inputs occupy only bounded levels of this hierarchy and that there are algorithms that handle in polynomial time each such bounded level
8 citations