In computational complexity theory, the Unique Games Conjecture is a conjecture made by Subhash Khot in 2002. The conjecture postulates that the problem of determining the value of a certain type of game, known as a unique game, has NP-hard algorithmic complexity. It has applications in the theory of hardness of approximation.
more from Wikipedia
Hardness of approximation
In computer science, hardness of approximation is a field that studies the algorithmic complexity of finding near-optimal solutions to optimization problems. It complements the study of approximation algorithms by proving, for certain problems, a limit on the factors with which their solution can be efficiently approximated.
more from Wikipedia
Linear programming relaxation
In mathematics, the linear programming relaxation of a 0-1 integer program is the problem that arises by replacing the constraint that each variable must be 0 or 1 by a weaker constraint, that each variable belong to the interval [0,1 0,1]. That is, for each constraint of the form of the original integer program, one instead uses a pair of linear constraints The resulting relaxation is a linear program, hence the name.
more from Wikipedia
NP-hard
NP-hard, in computational complexity theory, is a class of problems that are, informally, "at least as hard as the hardest problems in NP". A problem H is NP-hard if and only if there is an NP-complete problem L that is polynomial time Turing-reducible to H (i.e. , L¿¿¿TH). In other words, L can be solved in polynomial time by an oracle machine with an oracle for H.
more from Wikipedia
Satisfiability
In mathematical logic, satisfiability and validity are elementary concepts of semantics. A formula is satisfiable if it is possible to find an interpretation that makes the formula true. A formula is valid if all interpretations make the formula true. The opposites of these concepts are unsatisfiability and invalidity, that is, a formula is unsatisfiable if none of the interpretations make the formula true, and invalid if some such interpretation makes the formula false.
more from Wikipedia
Approximation algorithm
In computer science and operations research, approximation algorithms are algorithms used to find approximate solutions to optimization problems. Approximation algorithms are often associated with NP-hard problems; since it is unlikely that there can ever be efficient polynomial time exact algorithms solving NP-hard problems, one settles for polynomial time sub-optimal solutions.
more from Wikipedia
Pi
The number ¿ is a mathematical constant that is the ratio of a circle's circumference to its diameter. The constant, sometimes written pi, is approximately equal to 3.14159. It has been represented by the Greek letter "¿" since the mid-18th century.
more from Wikipedia
Permutation
In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting (rearranging) objects or values. Informally, a permutation of a set of objects is an arrangement of those objects into a particular order. For example, there are six permutations of the set {1,2,3}, namely (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), and (3,2,1). One might define an anagram of a word as a permutation of its letters.
more from Wikipedia