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In computational complexity, the logarithmic time hierarchy (LH) is the complexity class of all computational problems solvable in a logarithmic amount of computation time on an alternating Turing machine with a bounded number of alternations. It is a particular case of a bounded alternating Turing machine hierarchy. It is equal to FO and to FO ...
L (complexity) In computational complexity theory, L (also known as LSPACE, LOGSPACE or DLOGSPACE) is the complexity class containing decision problems that can be solved by a deterministic Turing machine using a logarithmic amount of writable memory space. [1][2] Formally, the Turing machine has two tapes, one of which encodes the input and ...
The time complexity of calculating all primes below n in the random access machine model is O(n log log n) operations, a direct consequence of the fact that the prime harmonic series asymptotically approaches log log n. It has an exponential time complexity with regard to length of the input, though, which makes it a pseudo-polynomial algorithm ...
Since this happens O(p) times, the total time complexity is O(p 3). A more efficient multiplication algorithm is the Schönhage–Strassen algorithm, which is based on the Fast Fourier transform. It only requires O(p log p log log p) time to square a p-bit number. This reduces the complexity to O(p 2 log p log log p) or Õ(p 2). [6]
Appearance. In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. [ 1 ] Particular focus is given to computation time (generally measured by the number of needed elementary operations) and memory storage requirements. The complexity of a problem is the complexity of ...
Polylogarithmic function. In mathematics, a polylogarithmic function in n is a polynomial in the logarithm of n, [1] The notation logkn is often used as a shorthand for (log n)k, analogous to sin2θ for (sin θ)2. In computer science, polylogarithmic functions occur as the order of time for some data structure operations.
A log–log plot of y = x (blue), y = x 2 (green), and y = x 3 (red). Note the logarithmic scale markings on each of the axes, and that the log x and log y axes (where the logarithms are 0) are where x and y themselves are 1. Comparison of linear, concave, and convex functions when plotted using a linear scale (left) or a log scale (right).
A demo of Graham's scan to find a 2D convex hull. Graham's scan is a method of finding the convex hull of a finite set of points in the plane with time complexity O (n log n). It is named after Ronald Graham, who published the original algorithm in 1972. [1] The algorithm finds all vertices of the convex hull ordered along its boundary.