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Computer Science › Computational complexity
Class of algorithms that find approximate solutions to optimization problems
In computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to optimization problems (in particular NP-hard problems) with provable guarantees on the distance of the returned solution to the optimal one.
Computer Science › Computational complexity
Function computable with bounded loops
In computability theory, a primitive recursive function is, roughly speaking, a function that can be computed by a computer program whose loops are all "for" loops (that is, an upper bound of the number of iterations of every loop is fixed before entering the loop).
Computer Science › Computational complexity
Cosmological theory
In physics, cosmology, and metaphysics, the mathematical universe hypothesis (MUH), also known as the ultimate ensemble theory, is a speculative "theory of everything" (TOE) proposed by cosmologist Max Tegmark. According to the hypothesis, the universe is a mathematical object in and of itself.
Computer Science › Computational complexity
Impossible task in computing
In mathematics and computer science, the Entscheidungsproblem (German for 'decision problem'; pronounced [ɛntˈʃaɪ̯dʊŋspʁoˌbleːm]) is a challenge posed by David Hilbert and Wilhelm Ackermann in 1928.
Computer Science › Computational complexity
On short connecting nets with added points
In combinatorial mathematics, the Steiner tree problem, or minimum Steiner tree problem, named after Jakob Steiner, is an umbrella term for a class of problems in combinatorial optimization.
Computer Science › Computational complexity
Subfield of mathematical topology
Algorithmic topology, or computational topology, is a subfield of topology with an overlap with areas of computer science, in particular, computational geometry and computational complexity theory.
Computer Science › Computational complexity
In modern computer science and statistics, the complexity index of a function denotes the level of informational content, which in turn affects the difficulty of learning the function from examples. This is different from computational complexity, which is the difficulty to compute a function.
Computer Science › Computational complexity
Number of edge slopes in graph drawing
In graph drawing and geometric graph theory, the slope number of a graph is the minimum possible number of distinct slopes of edges in a drawing of the graph in which vertices are represented as points in the Euclidean plane and edges are represented as line segments that do not pass through any non-incident vertex.
Computer Science › Computational complexity
Integer that is a perfect square modulo some integer
In number theory, an integer q is a quadratic residue modulo n if it is congruent to a perfect square modulo n; that is, if there exists an integer x such that x2≡q(modn). Otherwise, q is a quadratic nonresidue modulo n.
Computer Science › Computational complexity
Concept in computability theory
In computability theory, the μ-operator, minimization operator, or unbounded search operator searches for the least natural number with a given property. Adding the μ-operator to the primitive recursive functions makes it possible to define all computable functions.
Computer Science › Computational complexity
In computational complexity theory, a sparse language is a formal language (a set of strings) such that the complexity function, counting the number of strings of length n in the language, is bounded by a polynomial function of n.
Computer Science › Computational complexity
Theorem in computability theory
In computability theory, Post's theorem, named after Emil Post, describes the connection between the arithmetical hierarchy and the Turing degrees.
