The Christofides algorithm achieves a ratio of 1. 5.

The Christofides algorithm was one of the first approximation algorithms, and was in part responsible for drawing attention to approximation algorithms as a practical approach to intractable problems.

As a matter of fact, the term " algorithm " was not commonly extended to approximation algorithms until later ; the Christofides algorithm was initially referred to as the Christofides heuristic.

* The Christofides algorithm

However, it is a long-standing ( since 1975 ) open problem to improve the Christofides approximation factor of 1. 5 for general metric TSP to a smaller constant.

The Cyprus News Agency was officially established on February 16, 1976 at the initiative of the then Director General of the Cyprus Broadcasting Corporation ( CyBC ) Andreas Christofides, who saw the need for a national news agency for Cyprus.

With the official launching of CNA, Christofides appointed Andreas Hadjipapas, a journalist working for CyBC and correspondent for UPI and AFP in Cyprus, as chief editor of the Agency.

From this follows a simple algorithm, which can be stated in a high-level description English prose, as:

The algorithm proceeds as follows.

If the arguments are both greater than zero then the algorithm can be written in more elementary terms as follows:

The algorithm is as follows: eliminate x from all equations below, and then eliminate y from all equations below.

The formal algorithm to compute from follows.

The algorithm works as follows.

Pseudocode of the complete algorithm follows, where the arrays are zero-based:

The algorithm is as follows:

The equivalence of the two definitions follows from the fact that an algorithm on such a non-deterministic machine consists of two phases, the first of which consists of a guess about the solution which is generated in a non-deterministic way, while the second consists of a deterministic algorithm which verifies or rejects the guess as a valid solution to the problem.

The pigeonhole algorithm works as follows:

The algorithm works as follows:

The processor follows a fixed algorithm: assuming a stylesheet has already been read and prepared, the processor builds a source tree from the input XML document.

The algorithm is as follows: take any number, square it, remove the middle digits of the resulting number as the " random number ", then use that number as the seed for the next iteration.

The algorithm in pseudocode is as follows:

To show this, first note that every problem which is in both RP and co-RP has a Las Vegas algorithm as follows:

The algorithm essentially works as follows ( this is actually a description of the Metropolis algorithm, a special case of Metropolis – Hastings ):

This algorithm can be schematized as follows.

The steps of Grover's algorithm are given as follows.

The encryption algorithm works as follows: to encrypt a message to Alice under her public key,

The decryption algorithm works as follows: to decrypt a ciphertext with her private key,

The algorithm uses a queue data structure to store intermediate results as it traverses the graph, as follows:

The algorithm is as follows.

This is a serious problem with Algorithm I and is due to catastrophic cancellation in the subtraction of two similar numbers at the final stage of the algorithm.

A stable one-pass algorithm exists, similar to the one above, that computes:

He also was the original author of rzip, which uses a similar algorithm to rsync.

In automatic systems this can be done using a binary search algorithm or interpolation search ; manual searching may be performed using a roughly similar procedure, though this will often be done unconsciously.

A sorting algorithm ( similar to quicksort ):

A limitation of modeling fractals is that resemblance of a fractal model to a natural phenomenon does not prove that the phenomenon being modeled is formed by a process similar to the modeling algorithm.

The well-known radix-2 Cooley – Tukey algorithm, for N a power of 2, can compute the same result with only ( N / 2 ) log < sub > 2 </ sub > N complex multiplies ( again, ignoring simplifications of multiplications by 1 and similar ) and N log < sub > 2 </ sub > N complex additions.

A similar fact takes place for particular computational tasks, like the search problem, for which Grover's algorithm is optimal.

Path vector routing is discussed in RFC 1322 ; the path vector routing algorithm is somewhat similar to the distance vector algorithm in the sense that each border router advertises the destinations it can reach to its neighboring router.

When the critical section is longer than a few source code lines or involves lengthy looping, an embedded / real-time algorithm must resort to using mechanisms identical or similar to those available on general-purpose operating systems, such as semaphores and OS-supervised interprocess messaging.

SNOBOL4 pattern-matching uses a backtracking algorithm similar to that used in the logic programming language Prolog, which provides pattern-like constructs via DCGs.

It fundamentally improves on the Soundex algorithm by using information about variations and inconsistencies in English spelling and pronunciation to produce a more accurate encoding, which does a better job of matching words and names which sound similar.

It is similar to the μ-law algorithm used in North America and Japan.

It is similar to the A-law algorithm used in regions where digital telecommunication signals are carried on E-1 circuits, e. g. Europe.

This algorithm is guaranteed to converge to an image, and it should appear similar to the original image.

In modern Z-buffer systems, similar benefits can be gained through rough front-to-back sorting ( approaching the ' reverse painters algorithm '), early Z-reject ( in conjunction with hierarchical Z ), and less common deferred rendering techniques possible on programmable GPUs.

Compare this to heuristic, a similar concept used in mathematical discourse, psychology, and computer science, particularly in algorithm design.

* Midpoint circle algorithm, a similar algorithm for drawing circles

The resulting algorithm is formally similar, except that every dot product is replaced by a nonlinear kernel function.

A pattern-based modeling approach can thus be seen as an image construction algorithm, where the patterns of the training image are used, and tiled next to each other such that a new image with similar characteristics / features is generated.

Automata theory also studies if there exist any effective algorithm or not to solve problems similar to the following list.

The current algorithm with the lowest known exponent k is a generalization of the Coppersmith – Winograd algorithm that has an asymptotic complexity of O ( n < sup > 2. 3727 </ sup >) thanks to Vassilevska Williams .< ref > The original algorithm was presented by Don Coppersmith and Shmuel Winograd in 1990, has an asymptotic complexity of O ( n < sup > 2. 376 </ sup >).</ ref > This algorithm, and the Coppersmith-Winograd algorithm on which it is based, are similar to Strassen's algorithm: a way is devised for multiplying two k × k-matrices with fewer than k < sup > 3 </ sup > multiplications, and this technique is applied recursively.