# Category: Approximation algorithms

Vertex k-center problem
The vertex k-center problem is a classical NP-hard problem in computer science. It has application in facility location and clustering. Basically, the vertex k-center problem models the following real
Minimum k-cut
In mathematics, the minimum k-cut, is a combinatorial optimization problem that requires finding a set of edges whose removal would partition the graph to at least k connected components. These edges
Multi-fragment algorithm
The multi-fragment (MF) algorithm is a heuristic or approximation algorithm for the travelling salesman problem (TSP) (and related problems). This algorithm is also sometimes called the "greedy algori
Property testing
In computer science, a property testing algorithm for a decision problem is an algorithm whose query complexity to its input is much smaller than the instance size of the problem. Typically property t
Baker's technique
In theoretical computer science, Baker's technique is a method for designing polynomial-time approximation schemes (PTASs) for problems on planar graphs. It is named after Brenda Baker, who announced
Nearest neighbour algorithm
The nearest neighbour algorithm was one of the first algorithms used to solve the travelling salesman problem approximately. In that problem, the salesman starts at a random city and repeatedly visits
Shortest common supersequence problem
In computer science, the shortest common supersequence of two sequences X and Y is the shortest sequence which has X and Y as subsequences. This is a problem closely related to the longest common subs
Submodular set function
In mathematics, a submodular set function (also known as a submodular function) is a set function whose value, informally, has the property that the difference in the incremental value of the function
Bidimensionality
Bidimensionality theory characterizes a broad range of graph problems (bidimensional) that admit efficient approximate, fixed-parameter or kernel solutions in a broad range of graphs. These graph clas
(1+ε)-approximate nearest neighbor search
(1+ε)-approximate nearest neighbor search is a special case of the nearest neighbor search problem. The solution to the (1+ε)-approximate nearest neighbor search is a point or multiple points within d
K-approximation of k-hitting set
In computer science, k-approximation of k-hitting set is an approximation algorithm for weighted hitting set. The input is a collection S of subsets of some universe T and a mapping W from T to non-ne
Convex volume approximation
In the analysis of algorithms, several authors have studied the computation of the volume of high-dimensional convex bodies, a problem that can also be used to model many other problems in combinatori
Karloff–Zwick algorithm
The Karloff–Zwick algorithm, in computational complexity theory, is a randomised approximation algorithm taking an instance of MAX-3SAT Boolean satisfiability problem as input. If the instance is sati
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.
APX
In computational complexity theory, the class APX (an abbreviation of "approximable") is the set of NP optimization problems that allow polynomial-time approximation algorithms with approximation rati
Polynomial-time approximation scheme
In computer science (particularly algorithmics), a polynomial-time approximation scheme (PTAS) is a type of approximation algorithm for optimization problems (most often, NP-hard optimization problems
Metric k-center
In graph theory, the metric k-center or metric facility location problem is a combinatorial optimization problem studied in theoretical computer science. Given n cities with specified distances, one w
Methods of successive approximation
Mathematical methods relating to successive approximation include the following: * Babylonian method, for finding square roots of numbers * Fixed-point iteration * Means of finding zeros of functio
Christofides algorithm
The Christofides algorithm or Christofides–Serdyukov algorithm is an algorithm for finding approximate solutions to the travelling salesman problem, on instances where the distances form a metric spac
Farthest-first traversal
In computational geometry, the farthest-first traversal of a compact metric space is a sequence of points in the space, where the first point is selected arbitrarily and each successive point is as fa
Set cover problem
The set cover problem is a classical question in combinatorics, computer science, operations research, and complexity theory. It is one of Karp's 21 NP-complete problems shown to be NP-complete in 197
Fully polynomial-time approximation scheme
A fully polynomial-time approximation scheme (FPTAS) is an algorithm for finding approximate solutions to function problems, especially optimization problems. An FPTAS takes as input an instance of th
Approximation-preserving reduction
In computability theory and computational complexity theory, especially the study of approximation algorithms, an approximation-preserving reduction is an algorithm for transforming one optimization p
L-reduction
In computer science, particularly the study of approximation algorithms, an L-reduction ("linear reduction") is a transformation of optimization problems which linearly preserves approximability featu
Unique games conjecture
In computational complexity theory, the unique games conjecture (often referred to as UGC) is a conjecture made by Subhash Khot in 2002. The conjecture postulates that the problem of determining the a
PTAS reduction
In computational complexity theory, a PTAS reduction is an approximation-preserving reduction that is often used to perform reductions between solutions to optimization problems. It preserves the prop
Method of conditional probabilities
In mathematics and computer science, the probabilistic method is used to prove the existence of mathematical objects with desired combinatorial properties. The proofs are probabilistic — they work by
GNRS conjecture
In theoretical computer science and metric geometry, the GNRS conjecture connects the theory of graph minors, the stretch factor of embeddings, and the approximation ratio of multi-commodity flow prob
Gap reduction
In computational complexity theory, a gap reduction is a reduction to a particular type of decision problem, known as a c-gap problem. Such reductions provide information about the hardness of approxi
Approximation algorithm
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 g
Token reconfiguration
In computational complexity theory and combinatorics, the token reconfiguration problem is a reconfiguration problem on a graph with both an initial and desired state for tokens. Given a graph , an in
Nearest neighbor search
Nearest neighbor search (NNS), as a form of proximity search, is the optimization problem of finding the point in a given set that is closest (or most similar) to a given point. Closeness is typically
Minimum relevant variables in linear system
MINimum Relevant Variables in Linear System (Min-RVLS) is a problem in mathematical optimization. Given a linear program, it is required to find a feasible solution in which the number of non-zero var
Domination analysis
Domination analysis of an approximation algorithm is a way to estimate its performance, introduced by Glover and Punnen in 1997. Unlike the classical approximation ratio analysis, which compares the n
Alpha max plus beta min algorithm
The alpha max plus beta min algorithm is a high-speed approximation of the square root of the sum of two squares. The square root of the sum of two squares, also known as Pythagorean addition, is a us
Max/min CSP/Ones classification theorems
In computational complexity theory, a branch of computer science, the Max/min CSP/Ones classification theorems state necessary and sufficient conditions that determine the complexity classes of proble