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An integer relation algorithm is an algorithm for finding integer relations. Specifically, given a set of real numbers known to a given precision, an integer relation algorithm will either find an integer relation between them, or will determine that no integer relation exists with coefficients whose magnitudes are less than a certain upper bound .
NC = P problem The P vs NP problem is a major unsolved question in computer science that asks whether every problem whose solution can be quickly verified by a computer (NP) can also be quickly solved by a computer (P). This question has profound implications for fields such as cryptography, algorithm design, and computational theory. [1]
Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations.
In computer science, integer sorting is the algorithmic problem of sorting a collection of data values by integer keys. Algorithms designed for integer sorting may also often be applied to sorting problems in which the keys are floating point numbers, rational numbers, or text strings. [1]
Computational geometry applies computer algorithms to representations of geometrical objects. Theoretical computer science includes areas of discrete mathematics relevant to computing. It draws heavily on graph theory and mathematical logic. Included within theoretical computer science is the study of algorithms and data structures.
The algorithm will determine, for any instance of the problem, whether a stable matching exists, and if so, will find such a matching. Irving's algorithm has O( n 2 ) complexity , provided suitable data structures are used to implement the necessary manipulation of the preference lists and identification of rotations.
An early successful application of the LLL algorithm was its use by Andrew Odlyzko and Herman te Riele in disproving Mertens conjecture. [5]The LLL algorithm has found numerous other applications in MIMO detection algorithms [6] and cryptanalysis of public-key encryption schemes: knapsack cryptosystems, RSA with particular settings, NTRUEncrypt, and so forth.
Some properties are now given about integer relations definable in Presburger Arithmetic. For the sake of simplicity, all relations considered in this section are over non-negative integers. A relation is Presburger-definable if and only if it is a semilinear set. [14]