Concepts inOptimal algorithms and inapproximability results for every CSP?

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

Unique games conjecture

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

Semidefinite programming

Semidefinite programming (SDP) is a subfield of convex optimization concerned with the optimization of a linear objective function over the intersection of the cone of positive semidefinite matrices with an affine space, i.e. , a spectrahedron. Semidefinite programming is a relatively new field of optimization which is of growing interest for several reasons.  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

Constraint satisfaction problem

Constraint satisfaction problems (CSP)s are mathematical problems defined as a set of objects whose state must satisfy a number of constraints or limitations. CSPs represent the entities in a problem as a homogeneous collection of finite constraints over variables, which is solved by constraint satisfaction methods.  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

Time complexity

In computer science, the time complexity of an algorithm quantifies the amount of time taken by an algorithm to run as a function of the size of the input to the problem. The time complexity of an algorithm is commonly expressed using big O notation, which suppresses multiplicative constants and lower order terms. When expressed this way, the time complexity is said to be described asymptotically, i.e. , as the input size goes to infinity.  more from Wikipedia