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A Pairwise Algorithm is an algorithmic technique with its origins in Dynamic programming. Pairwise algorithms have several uses including comparing a
Pairwise_Algorithm
Algorithmic technique
those FFTs. In pseudocode, the pairwise summation algorithm for an array x of length n ≥ 0 can be written: s = pairwise(x[1...n]) if n ≤ N base case: naive
Pairwise_summation
Important algorithms in numerical statistics
H.; LeVeque, Randall J. (November 1979). "Updating Formulae and a Pairwise Algorithm for Computing Sample Variances" (PDF). Department of Computer Science
Algorithms for calculating variance
Algorithms_for_calculating_variance
Use of machine learning to rank items
measures have to be used. For example the SoftRank algorithm. LambdaMART is a pairwise algorithm which has been empirically shown to approximate listwise
Learning_to_rank
Algorithm that arranges lists in order
In computer science, a sorting algorithm is an algorithm that puts elements of a list into an order. The most frequently used orders are numerical order
Sorting_algorithm
Algorithms which recursively solve subproblems
simple loop that adds each datum to a single variable, or by a D&C algorithm called pairwise summation that breaks the data set into two halves, recursively
Divide-and-conquer_algorithm
Algorithm in numerical analysis
a larger base case. The equivalent of pairwise summation is used in many fast Fourier transform (FFT) algorithms and is responsible for the logarithmic
Kahan_summation_algorithm
Algorithm for supervised learning of binary classifiers
In machine learning, the perceptron is an algorithm for supervised learning of binary classifiers. A binary classifier is a function that can decide whether
Perceptron
Vector quantization algorithm minimizing the sum of squared deviations
\|\cdot \|} is the usual L2 norm . This is equivalent to minimizing the pairwise squared deviations of points in the same cluster: a r g m i n S ∑ i =
K-means_clustering
Two numbers without shared prime factors
the set is said to be pairwise coprime (or pairwise relatively prime, mutually coprime or mutually relatively prime). Pairwise coprimality is a stronger
Coprime_integers
Algorithm that employs a degree of randomness as part of its logic or procedure
derandomize geometric algorithms) the exploitation of limited independence in the random variables used by the algorithm, such as the pairwise independence used
Randomized_algorithm
Method for aligning biological sequences
The Needleman–Wunsch algorithm is an algorithm used in bioinformatics to align protein or nucleotide sequences. It was one of the first applications of
Needleman–Wunsch_algorithm
Discrete Fourier transform algorithm
most FFT algorithms, e.g., Cooley–Tukey, have excellent numerical properties as a consequence of the pairwise summation structure of the algorithms. The upper
Fast_Fourier_transform
Machine learning technique
that pairwise preferences can be substituted with pointwise rewards. Kahneman-Tversky optimization (KTO) is another direct alignment algorithm drawing
Reinforcement learning from human feedback
Reinforcement_learning_from_human_feedback
About simultaneous modular congruences
the product of these integers, under the condition that the divisors are pairwise coprime (no two divisors share a common factor other than 1). The theorem
Chinese_remainder_theorem
Algorithm in computer graphics
polygons as input. In its original form, the algorithm is divided into three phases: In the first phase, pairwise intersections between edges of the polygons
Greiner–Hormann clipping algorithm
Greiner–Hormann_clipping_algorithm
Process in bioinformatics that identifies equivalent sites within molecular sequences
[1]. Pairwise sequence alignment methods are used to find the best-matching piecewise (local or global) alignments of two query sequences. Pairwise alignments
Sequence_alignment
Sets with no element in common
is pairwise disjoint. A Helly family is a system of sets within which the only subfamilies with empty intersections are the ones that are pairwise disjoint
Disjoint_sets
Meta-algorithmic technique to choose an algorithm
to learn pairwise models between every pair of classes (here algorithms) and choose the class that was predicted most often by the pairwise models. We
Algorithm_selection
Problem in computational complexity theory
Unsolved problem in computer science Is there an algorithm to solve the 3SUM problem in time O ( n 2 − ϵ ) {\displaystyle O(n^{2-\epsilon })} , for some
3SUM
Process of comparing two entities to determine preference
Pairwise comparison generally is any process of comparing entities in pairs to judge which of each entity is preferred, or has a greater amount of some
Pairwise comparison (psychology)
Pairwise_comparison_(psychology)
Information used for message authentication and integrity checking
consists of three algorithms: A key generation algorithm selects a key from the key space uniformly at random. A MAC generation algorithm efficiently returns
Message_authentication_code
Least-weight tree connecting graph vertices
computationally-efficient algorithms. In a comparison model, in which the only allowed operations on edge weights are pairwise comparisons, Karger, Klein
Minimum_spanning_tree
Cryptographic protocol for instant messaging
server-side fan-out and avoids computing a shared group key. The algorithm relies upon secure pairwise communication channels between peers that provide confidentiality
Sender_Keys
Concept in computing
employ some of these ideas: The core of the protocol involves periodic, pairwise, inter-process interactions. The information exchanged during these interactions
Gossip_protocol
Algorithms for calculating square roots
Square root algorithms compute the non-negative square root S {\displaystyle {\sqrt {S}}} of a positive real number S {\displaystyle S} . Since all square
Square_root_algorithms
Computer science metric for string similarity
also denote a larger family of distance metrics. It is closely related to pairwise string alignments. The Levenshtein distance between two strings a , b {\displaystyle
Levenshtein_distance
Statistical method in data analysis
criterion, which specifies the dissimilarity of sets as a function of the pairwise distances of observations in the sets. The choice of metric as well as
Hierarchical_clustering
Java implementation of the Smith-Waterman algorithm with Gotoh's improvement for biological local pairwise sequence alignment using the affine gap penalty
JAligner
Classical problem in combinatorics
n=2^{(k+1)}-2} elements. The set system consists of k {\displaystyle k} pairwise disjoint sets S 1 , … , S k {\displaystyle S_{1},\ldots ,S_{k}} with sizes
Set_cover_problem
NP-hard problem in combinatorial optimization
also by many travelers) the task to find, for finitely many points whose pairwise distances are known, the shortest route connecting the points. Of course
Travelling_salesman_problem
Machine learning algorithm
equipped with pairwise dissimilarities such as categorical sequences. Decision trees are among the most popular machine learning algorithms given their
Decision_tree_learning
Term in computer science
the exact pairwise collision detection, this is highly trajectory dependent, and one almost has to use a numerical root-finding algorithm to compute
Collision_detection
Grouping a set of objects by similarity
analysis refers to a family of algorithms and tasks rather than one specific algorithm. It can be achieved by various algorithms that differ significantly
Cluster_analysis
r ≥ 2 pairwise distinct irreducible factors f 1 , … , f r {\displaystyle f_{1},\ldots ,f_{r}} each of degree d. We first describe an algorithm by Cantor
Factorization of polynomials over finite fields
Factorization_of_polynomials_over_finite_fields
System of rapid mental calculation
and finishing with the leftmost. Trachtenberg defined this algorithm with a kind of pairwise multiplication where two digits are multiplied by one digit
Trachtenberg_system
Set of methods for supervised statistical learning
classification using the kernel trick, representing the data only through a set of pairwise similarity comparisons between the original data points using a kernel
Support_vector_machine
Algorithm for searching sorted, infinite lists
current element being accessed. An algorithm based on exponentially increasing the search band solves global pairwise alignment for O ( n s ) {\displaystyle
Exponential_search
Criterion applied in hierarchical cluster analysis
{\displaystyle C_{j}} were next to be merged. At this point all of the current pairwise cluster distances are known. The recursive formula gives the updated cluster
Ward's_method
IEEE standard version
or 802.1X authentication, a shared secret key is generated, called the Pairwise Master Key (PMK). In PSK authentication, the PMK is actually the PSK, which
IEEE_802.11i-2004
Bioinformatics computer program
globally optimal solution. First, the algorithm computes a pairwise distance matrix between all pairs of sequences (pairwise sequence alignment). Next, a neighbor-joining
Clustal
Family of stochastic optimization methods
Estimation of distribution algorithms (EDAs), sometimes called probabilistic model-building genetic algorithms (PMBGAs), are stochastic optimization methods
Estimation of distribution algorithm
Estimation_of_distribution_algorithm
Greatest common divisor of polynomials
polynomial GCD may be computed as for the integer GCD, with the Euclidean algorithm using long division. The polynomial GCD is defined only up to the multiplication
Polynomial greatest common divisor
Polynomial_greatest_common_divisor
Agglomerative hierarchical clustering method
working example). The UPGMA algorithm constructs a rooted tree (dendrogram) that reflects the structure present in a pairwise similarity matrix (or a dissimilarity
UPGMA
similar proteins. Pairwise local structural alignment This tool takes as an input two proteins or binding sites. The ProBiS algorithm compares structures
ProBiS
Polynomial with no repeated root
_{k=1}^{n}a_{k}^{k}\,} where those of the ak that are non-constant are pairwise coprime square-free polynomials (here, two polynomials are said coprime
Square-free_polynomial
Optimization problem in kidney donation programs
maximum-cardinality pairwise exchange is equivalent to finding a maximum cardinality matching in that undirected graph. Moreover, when only pairwise exchanges are
Optimal_kidney_exchange
Type of sports tournament
this algorithm realizes every possible combination of them (equivalently, that all pairs realized are pairwise different). First, the algorithm obviously
Round-robin_tournament
Statistical model for pairwise comparisons
The Bradley–Terry model is a probability model for the outcome of pairwise comparisons between items, teams, or objects. Given a pair of items i and j
Bradley–Terry_model
Whether one vertex can be reached from another in a graph
remainder of this article focuses on the more difficult problem of determining pairwise reachability in a directed graph (which, incidentally, need not be symmetric)
Reachability
Stack-based method for clustering
In the theory of cluster analysis, the nearest-neighbor chain algorithm is an algorithm that can speed up several methods for agglomerative hierarchical
Nearest-neighbor chain algorithm
Nearest-neighbor_chain_algorithm
Clustering algorithm minimizing the sum of distances to k representatives
that the programmer must specify k before the execution of a k-medoids algorithm). The "goodness" of the given value of k can be assessed with methods
K-medoids
Set of edges without common vertices
it can be done using Edmonds' blossom algorithm. Given a graph G = (V, E), a matching M in G is a set of pairwise non-adjacent edges, none of which are
Matching_(graph_theory)
Mathematical modelling alogorithm
method of data handling (GMDH) is a family of inductive, self-organizing algorithms for mathematical modelling that automatically determines the structure
Group_method_of_data_handling
Pairwise-comparison electoral system
Condorcet method. Condorcet methods use pairwise counting. For each possible pair of candidates, one pairwise count indicates how many voters prefer one
Condorcet_method
Two or more species influencing each other's evolution
pressures drive an evolutionary arms race between the species involved. Pairwise or specific coevolution, between exactly two species, is not the only possibility;
Coevolution
Area of discrete mathematics
is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices
Graph_theory
Algorithm analysis method
good partition into clusters with small pairwise distances between points in the same cluster. Lloyd's algorithm is widely used and very fast in practice
Smoothed_analysis
Point minimizing sum of distances to given points
property follows from the fact that the geometric median is defined only from pairwise distances, and does not depend on the system of orthogonal Cartesian coordinates
Geometric_median
Cluster analysis algorithm
non-Euclidean or categorical data. However, because it involves evaluating pairwise dissimilarities and repeatedly searching for representative points, it
K-medians_clustering
Field in statistics pertaining to establishing cause and effect
geophysics using the PC-stable algorithm (a variant of the original PC algorithm) and in dynamical systems using pairwise asymmetric inference (a variant
Exploratory_causal_analysis
Machine learning framework for portfolio construction
traditional quadratic optimization methods, including the Critical Line Algorithm (CLA) of Markowitz. HRP addresses three central issues commonly associated
Hierarchical_Risk_Parity
Numerical linear algebra algorithm
In numerical linear algebra, the Jacobi eigenvalue algorithm is an iterative method for the calculation of the eigenvalues and eigenvectors of a real
Jacobi_eigenvalue_algorithm
Set preferred to any other by a majority
defined as the smallest set such that every candidate inside the set S pairwise defeats every candidate outside S. Alternatively, it can be defined as
Smith_set
Problem of grouping into triples
2-dimensional matching is then a matching in the graph G, that is, a set of pairwise non-adjacent edges. Hence 3-dimensional matchings can be interpreted as
3-dimensional_matching
Algorithmic process of solving equations
computer science, specifically automated reasoning, unification is an algorithmic process of solving equations between symbolic expressions, each of the
Unification (computer science)
Unification_(computer_science)
The pairwise sorting network is a sorting network discovered and published by Ian Parberry in 1992 in Parallel Processing Letters. The pairwise sorting
Pairwise_sorting_network
Evolutionary algorithm
Mutation amounts to adding a random vector, a perturbation with zero mean. Pairwise dependencies between the variables in the distribution are represented
CMA-ES
Type of heuristic technique
Sampling (D-TS) algorithm has been proposed for dueling bandits, a variant of traditional MAB, where feedback comes in the form of pairwise comparison. Probability
Thompson_sampling
Surface area of a biomolecule accessible to a solvent
typically calculated using the 'rolling ball' algorithm developed by Shrake & Rupley in 1973. This algorithm uses a sphere (of solvent) of a particular radius
Accessible_surface_area
the pairwise distances computed, only about 16% will actually be less than or equal to r c {\displaystyle r_{c}} . In other words, 84% of all pairwise distance
Cell_lists
Function for machine learning algorithms
examples. It was conceived by Google researchers for their prominent FaceNet algorithm for face detection. Triplet loss is designed to support metric learning
Triplet_loss
Process in machine learning and statistics
involves two variables, it thus uses pairwise joint probabilities which are more robust. In certain situations the algorithm may underestimate the usefulness
Feature_selection
Class of semi-supervised learning algorithms
possible solutions. Examples of constrained clustering algorithms include: COP K-means PCKmeans (Pairwise Constrained K-means) CMWK-Means (Constrained Minkowski
Constrained_clustering
Sonnhammer (2001). "Automatic clustering of orthologs and in-paralogs from pairwise species comparisons". Journal of Molecular Biology. 314 (5): 1041–1052
Inparanoid
Collective operation in parallel computing
all-to-all algorithm. We consider a single-ported full-duplex machine throughout this article. On such a machine, an all-to-all algorithm requires at
All-to-all_(parallel_pattern)
Discrete analog of a derivative
highest-order term. Given the assumption above and m − 1 pairwise differences (resulting in a total of m pairwise differences for S(x)), it can be found that: Δ
Finite_difference
Topics referred to by the same term
density matrix renormalization group numerical technique Superblock algorithm, in the pairwise summation numerical analysis Superblock, of pixels, for example
Superblock
Agglomerative hierarchical clustering method
in each cluster) that are closest to each other. The shortest of these pairwise distances that remain at any step causes the two clusters whose elements
Single-linkage_clustering
Software for sequence alignment
accurate tree via the Kimura distance. Thus, the algorithm analysis involves the initial subprocedures of pairwise distance calculations and progressive alignment;
MUSCLE_(alignment_software)
Single-winner electoral system
voters rank 5 candidates. The pairwise preferences have to be computed first. For example, when comparing A and B pairwise, there are 5+5+3+7=20 voters
Schulze_method
haplotypes. The diversity is defined as the total number of differences in all pairwise comparison between haplotypes. The difference between a pair of haplotypes
Tag_SNP
Aligning molecular sequences using sequence and structural information
the distance matrix, which is a two-dimensional matrix containing all pairwise distances between some subset of the atoms in each structure (such as the
Structural_alignment
Process of reducing the number of random variables under consideration
variance unfolding (MVU). The central idea of MVU is to exactly preserve all pairwise distances between nearest neighbors (in the inner product space) while
Dimensionality_reduction
Quality measure in cluster analysis
running the algorithm for different numbers of clusters. This algorithm needs pairwise distances and is typically implemented with a pairwise distance matrix
Silhouette_(clustering)
Algorithms for matrix decomposition
ISSN 2364-415X. Youdong Guo & Timothy E. Holy (2025). "An optimal pairwise merge algorithm improves the quality and consistency of nonnegative matrix factorization"
Non-negative matrix factorization
Non-negative_matrix_factorization
Algorithm for measuring similarity between temporal sequences
In time series analysis, dynamic time warping (DTW) is an algorithm for measuring similarity between two temporal sequences, which may vary in speed.
Dynamic_time_warping
Sequence of points far from previous points
where the distance from a point to a set is defined as the minimum of the pairwise distances to points in the set. A given space may have many different farthest-first
Farthest-first_traversal
alignment software is a compilation of software tools and web portals used in pairwise sequence alignment and multiple sequence alignment. See structural alignment
List of sequence alignment software
List_of_sequence_alignment_software
Agglomerative hierarchical clustering method
{\displaystyle (a,b,c,d,e)} and the following matrix D 1 {\displaystyle D_{1}} of pairwise distances between them: In this example, D 1 ( a , b ) = 17 {\displaystyle
Complete-linkage_clustering
Software testing method
pairwise testing is a combinatorial method of software testing that, for each pair of input parameters to a system (typically, a software algorithm)
All-pairs_testing
Set of machine learning methods
the kernels. The weighting is learned in the algorithm. Other examples of fixed rules include pairwise kernels, which are of the form k ( ( x 1 i , x
Multiple_kernel_learning
Technique for selecting hash functions
In mathematics and computing, universal hashing (in a randomized algorithm or data structure) refers to selecting a hash function at random from a family
Universal_hashing
SuperPose is a freely available web server designed to perform both pairwise and multiple protein structure superpositions. The “Structural superposition”
SuperPose
enhancements to the speed and accuracy of MAFFT v7. The MAFFT algorithm works following these 5 steps Pairwise Alignment, Distance Calculation, Guide Tree Construction
MAFFT
Problem in computer science
Then, the set packing problem asks if some k subsets in the list are pairwise disjoint (in other words, no two of them share an element). More formally
Set_packing
Concept in modular arithmetic
X ≡ 4 (mod 7) X ≡ 6 (mod 11) has common solutions since 5,7 and 11 are pairwise coprime. A solution is given by X = t1 (7 × 11) × 4 + t2 (5 × 11) × 4 +
Modular multiplicative inverse
Modular_multiplicative_inverse
Method of partitioning data points into groups based on their similarity
framework in which a set of objects is partitioned into clusters based on pairwise similarity and dissimilarity information, without requiring the number
Correlation_clustering
Logic problem, AND of pairwise ORs
for solving constraint satisfaction problems with binary variables and pairwise constraints. They apply this technique to a problem of classroom scheduling
2-satisfiability
Alignment of more than two molecular sequences
problem. In 1989, based on Carrillo-Lipman Algorithm, Altschul introduced a practical method that uses pairwise alignments to constrain the n-dimensional
Multiple_sequence_alignment
PAIRWISE ALGORITHM
PAIRWISE ALGORITHM
PAIRWISE ALGORITHM
Boy/Male
Tamil
Morning, Dawn
Boy/Male
Sikh
Lord Guru
Girl/Female
Indian, Sanskrit
Beautiful Moon
Girl/Female
Hindu, Indian, Kannada, Telugu
Together; Precious
Boy/Male
Hindu, Indian, Marathi
Strength
Girl/Female
Tamil
Jaymini | ஜயà¯à®®à¯€à®¨à¯€
An ancient philosopher
Boy/Male
Indian, Punjabi, Sikh
Inner Support
Boy/Male
African, Arabic, Farsi
Merciful
Boy/Male
Indian, Sanskrit
Beloved Youth
Female
English
Variant spelling of English Lizzie, LIZZY means "God is my oath."
PAIRWISE ALGORITHM
PAIRWISE ALGORITHM
PAIRWISE ALGORITHM
PAIRWISE ALGORITHM
PAIRWISE ALGORITHM
a.
Having the tinctures exchanged mutually; thus, if the field is divided palewise, or and azure, and cross is borne counterchanged, that part of the cross which comes on the azure side will be or, and that on the or side will be azure.
n.
The art of calculating by nine figures and zero.
n.
Alt. of Parvise
n.
Alt. of Algorithm
adv.
Horizontally.
adv.
In the manner of a pale or pales; by perpendicular lines or divisions; as, to divide an escutcheon palewise.
v. t.
To join, as two coats of arms on one shield, palewise; hence, to join in honorable mention.
n.
The division of a shield palewise, or by a vertical line, esp. for the purpose of putting side by side the arms of husband and wife. See Impale, 3.
n.
One of the ordinaries or subordinaries having the form of a wedge, usually placed palewise, with the broadest end uppermost.
n.
The art of calculating with any species of notation; as, the algorithms of fractions, proportions, surds, etc.
n.
a court of entrance to, or an inclosed space before, a church; hence, a church porch; -- sometimes formerly used as place of meeting, as for lawyers.