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.

Set-Membership Type-1 Fuzzy Logic System Applied to Fault Classification in a Switch Machine

Abstract: This paper focuses on the classification of faults in an electromechanical switch machine, which is an equipment used for handling railroad switches. In this paper, we introduce the use of Set-Membership concept, derived from the adaptive filter theory, into the training procedure of type-1 and singleton/non-singleton fuzzy logic systems, in order to reduce computational complexity and to increase convergence speed. We also present different criteria for using along with Set-Membership. Furthermore, we discuss the usefulness of delta rule delta, local Lipschitz estimation, variable step size, and variable step size adaptive techniques to yield additional improvement in terms of computational complexity reduction and convergence speed. Based on data set provided by a Brazilian railway company, which covers the four possible faults in a switch machine, we present performance analysis in terms of classification ratio, convergence speed, and computational complexity reduction. The reported results show that the proposed models result in improved convergence speed, slightly higher classification ratio, and remarkable computation complexity reduction when we limit the number of epochs for training, which may be required due to real-time constraint or low computational resource availability.

Dispersion of Mass and the Complexity of Randomized Geometric Algorithms

Abstract: How much can randomness help computation? Motivated by this general question and by volume computation, one of the few instances where randomness provably helps, we analyze a notion of dispersion and connect it to asymptotic convex geometry. We obtain a nearly quadratic lower bound on the complexity of randomized volume algorithms for convex bodies in \mathbb{R}^n (the current best algorithm has complexity roughly n^4, conjectured to be n^3). Our main tools, dispersion of random determinants and dispersion of the length of a random point from a convex body, are of independent interest and applicable more generally; in particular, the latter is closely related to the variance hypothesis from convex geometry. This geometric dispersion also leads to lower bounds for matrix problems and property testing.

Generalized kolmogorov complexity and other dual complexity measures

Abstract: We construct and analyze some dual complexity measures that indicate the time it takes to obtain the desired object. The existence of optimal dual complexity measures is established. Various relations between dual measures and complexities are determined. The relationship of these measures to program quality is demonstrated.

Complexity of algorithms and computations

Abstract: A survey is given of some results on the complexity of algorithms and computations published up to 1973.