Algorithms and Complexity Theory

A quantum computer is a computer that represents and processes information using quantum states.

In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions and other mathematical objects.

It is still unknown (except for the case n = 2) if Whitehead's algorithm has polynomial time complexity.

analysis of algorithms

deterministic logarithmic-space algorithm for st-connectivity

alpha-beta pruning algorithm

synthesis and complexity of Boolean circuits

Ford-Fulkerson algorithm

Leader in the study of computational complexity

who designed the Shellsort sorting algorithm

fundamental contributions to the fields of combinatorial optimization, polyhedral combinatorics, discrete mathematics and the theory of computing

known for his contributions to computer programming, algorithms and data structure research

he is known for the Levenshtein distance and a Levenshtein algorithm, which he developed in 1965

was an American statistician, the rediscoverer of the Levenberg

He described the Hungarian method for the assignment problem

known for his work in algorithms and networks

one of the fathers of the LZ family of lossless data compression algorithms

who developed the LZ family of lossless data compression algorithms alongside Abraham Lempel

Along with Abraham Lempel and Jacob Ziv, he developed the lossless

He is best known for his work in graph theory

was a pioneer in convex optimization theory and mathematical programming

he devised the Christofides algorithm, an algorithm for finding approximate solutions to the travelling salesman problem

original author of the widely used nonlinear least squares fitting algorithm

used to detect community structure in complex systems

known for her work on sparse matrix algorithms

He did important work in scheduling theory, computational geometry

He is most noted for his co-invention and development of the Kalman filter, a mathematical algorithm

algorithmic information theory and computational complexity

Frank Harary (March 11, 1921, January 4, 2005) was an American mathematician, who specialized in graph theory.

Chayes is best known for her work on phase transitions in discrete mathematics and computer science, structural and dynamical properties of self-engineered networks, and algorithmic game theory.

Tollis) of the book Graph drawing: Algorithms for the visualization of graphs, and of the associated survey "Algorithms for drawing graphs: an annotated bibliography".

Page is the co-creator and namesake of PageRank, a search ranking algorithm for Google for which he received the Marconi Prize in 2004 along with co-writer Brin.

In graph theory, Lovász's notable contributions include the proofs of Kneser's conjecture and the Lovász local lemma, as well as the formulation of the Erdős-Faber-Lovász conjecture.

He is a professor at Tel Aviv University, notable for his contributions to computational geometry and combinatorial geometry, having authored hundreds of papers.

She is known for her work in algorithmic game theory and computational social choice.

Dorothea Wagner (born 1957) is a German computer scientist, known for her research in graph drawing, route planning, and social network analysis.

The critical path method (CPM), or critical path analysis (CPA), is an algorithm for scheduling a set of project activities.

Square root algorithms compute the non-negative square root

is a companding algorithm, primarily used in eight-bit PCM digital telecommunications systems in North America and Japan.

Samet is a pioneer in research on quadtrees and other multidimensional spatial data structures for sorting spatial information, and has written several well-received books.

This was the first known balanced binary search tree data structure.

Giorgio Buttazzo from the Sant'Anna School of Advanced Studies, Pisa, Italy was named Fellow of the Institute of Electrical and Electronics Engineers (IEEE) in 2012 for contributions to dynamic scheduling algorithms in real-time systems.

Lee, is a Taiwanese computer scientist known for his work in computational geometry.

Richard Ernest Bellman (August 26, 1920, March 19, 1984) was an American applied mathematician, who introduced dynamic programming in 1953, and made important contributions in other fields of mathematics, such as biomathematics.

Linear probing is a scheme in computer programming for resolving collisions in hash tables, data structures for maintaining a collection of key-value pairs and looking up the value associated with a given key.

He began conducting research in numerical analysis, and developed a number of concepts in service of early digital computers.

Collections of unique deltas are substantially more space-efficient than their non-encoded equivalents.

The Bailey-Borwein-Plouffe formula (BBP formula) is a formula for π.

The Lehmer random number generator (named after D. H. Lehmer)

In number theory, a branch of mathematics, the special number field sieve (SNFS)

In number theory, Dixon's factorization method

In 1997, an algorithm for solving a system using Cramer's rule with complexity equal to that of matrix multiplication was proposed.

is a primality test for Mersenne numbers

is a primality test, which can be used to determine whether a Fermat number is prime

is an algorithm for determining whether a number is prime

is an integer factorization algorithm

significantly reduces the numerical error in the total obtained by adding a sequence of finite-precision floating-point numbers

devised the test for Mersenne primes still used today

He also gave his name to Pépin's test, a test of primality for Fermat numbers

Together with Joep Kerbosch he invented the Bron-Kerbosch algorithm for the clique problem.

Fermat's factorization method tries to exploit this fact by guessing the first square

Dekker invented an algorithm that allows two processes to share a single-use resource without conflict

He invented a factorization method

SMA* or Simplified Memory Bounded A* is a shortest path algorithm based on the A* algorithm.

In mathematics, more specifically in numerical linear algebra, the biconjugate gradient method is an algorithm to solve systems of linear equations

Bellman-Ford algorithm is an algorithm that computes shortest paths from a single source vertex to all of the other vertices in a weighted digraph.

Kruskal's algorithm finds a minimum spanning forest of an undirected edge-weighted graph.

linear search or sequential search is a method for finding an element within a list.

Interpolation search is an algorithm for searching for a key in an array that has been ordered by numerical values assigned to the keys (key values).

Timsort is a hybrid, stable sorting algorithm, derived from merge sort and insertion sort, designed to perform well on many kinds of real-world data.

Introsort or introspective sort is a hybrid sorting algorithm that provides both fast average performance and (asymptotically) optimal worst-case performance.

Johnson's algorithm is a way to find the shortest paths between all pairs of vertices in an edge-weighted directed graph.

Tarjan's strongly connected components algorithm is an algorithm in graph theory for finding the strongly connected components (SCCs) of a directed graph.

Kosaraju-Sharir's algorithm (also known as Kosaraju's algorithm) is a linear time algorithm to find the strongly connected components of a directed graph.

simplex algorithm (or simplex method) is an algorithm for linear programming.

sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit.

Strassen algorithm, named after Volker Strassen, is an algorithm for matrix multiplication.

fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT), or its inverse (IDFT), of a sequence.

Miller-Rabin primality test or Rabin-Miller primality test is a probabilistic primality test: an algorithm which determines whether a given number is likely to be prime, similar to the Fermat primality test and the Solovay-Strassen primality test.

Bowyer-Watson algorithm is a method for computing the Delaunay triangulation of a finite set of points in any number of dimensions.

Fortune's algorithm is a sweep line algorithm for generating a Voronoi diagram from a set of points in a plane using O(n log n) time and O(n) space.

Bentley-Ottmann algorithm is a sweep line algorithm for listing all crossings in a set of line segments, i.e.

Borůvka's algorithm is a greedy algorithm for finding a minimum spanning tree in a graph, or a minimum spanning forest in the case of a graph that is not connected.

In computer science, the Hopcroft-Karp algorithm (sometimes more accurately called the Hopcroft-Karp-Karzanov algorithm) is an algorithm that takes a bipartite graph as input and produces a maximum-cardinality matching as output - a set of as many edges as possible with the property that no two edges share an endpoint.

Yen's algorithm computes single-source K-shortest loopless paths for a graph with non-negative edge cost.

Held-Karp algorithm, also called the Bellman-Held-Karp algorithm, is a dynamic programming algorithm proposed in 1962 independently by Bellman and by Held and Karp to solve the traveling salesman problem (TSP), in which the input is a distance matrix between a

Gaussian elimination, also known as row reduction, is an algorithm for solving systems of linear equations.

exponentiating by squaring is a general method for fast computation of large positive integer powers of a number, or more generally of an element of a semigroup, like a polynomial or a square matrix.

Horner's method (or Horner's scheme) is an algorithm for polynomial evaluation.

Interior-point methods (also referred to as barrier methods or IPMs) are algorithms for solving linear and non-linear convex optimization problems.

jump search or block search refers to a search algorithm for ordered lists.

Fibonacci search technique is a method of searching a sorted array using a divide and conquer algorithm that narrows down possible locations with the aid of Fibonacci numbers.

ternary search algorithm is a technique in computer science for finding the minimum or maximum of a unimodal function.

Shellsort, also known as Shell sort or Shell's method, is an in-place comparison sort.

Comb sort is a relatively simple sorting algorithm originally designed by Włodzimierz Dobosiewicz and Artur Borowy in 1980, later rediscovered (and given the name "Combsort") by Stephen Lacey and Richard Box in 1991. Comb sort improves on bubble sort in the sa

Aho-Corasick algorithm is a string-searching algorithm invented by Alfred V. Aho and Margaret J. Corasick in 1975. It is a kind of dictionary-matching algorithm that locates elements of a finite set of strings (the "dictionary") within an input text.

Levenshtein distance is a string metric for measuring the difference between two sequences.

Burrows-Wheeler transform (BWT) rearranges a character string into runs of similar characters, in a manner that can be reversed to recover the original string.

rotating calipers is an algorithm design technique that can be used to solve optimization problems including finding the width or diameter of a set of points.

Hungarian algorithm or Hungarian method is a combinatorial optimization algorithm that solves the assignment problem in polynomial time and which anticipated later primal-dual methods.

Dinic's algorithm or Dinitz's algorithm is a strongly polynomial algorithm for computing the maximum flow in a flow network, conceived in 1970 by Israeli (formerly Soviet) computer scientist Yefim Dinitz.

Karger's algorithm is a randomized algorithm to compute a minimum cut of a connected graph.

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 space (they are symmetric and obey the triangle inequality).

Viterbi algorithm is a dynamic programming algorithm that finds the most likely sequence of hidden events that would explain a sequence of observed events.

Baum-Welch algorithm is a special case of the expectation-maximization algorithm used to find the unknown parameters of a hidden Markov model (HMM).

Karmarkar's algorithm is an algorithm introduced by Narendra Karmarkar in 1984 for solving linear programming problems.

Ukkonen's algorithm is a linear-time, online algorithm for constructing suffix trees, proposed by Esko Ukkonen in 1995. The algorithm begins with an implicit suffix tree containing the first character of the string.

smoothsort is a comparison-based sorting algorithm.

patience sorting is a sorting algorithm inspired by, and named after, the card game patience.

Louvain method for community detection is a greedy optimization method intended to extract non-overlapping communities from large networks created by Blondel et al.

Girvan-Newman algorithm (named after Michelle Girvan and Mark Newman) is a hierarchical method used to detect communities in complex systems.

Bron-Kerbosch algorithm is an enumeration algorithm for finding all maximal cliques in an undirected graph.

Levenberg-Marquardt algorithm (LMA or just LM), also known as the damped least-squares (DLS) method, is used to solve non-linear least squares problems.

Mean shift is a non-parametric feature-space mathematical analysis technique for locating the maxima of a density function, a so-called mode-seeking algorithm.

Cohen-Sutherland algorithm is an algorithm used for line clipping.

Ramer-Douglas-Peucker algorithm, also known as the Douglas-Peucker algorithm and iterative end-point fit algorithm, is an algorithm that decimates a curve composed of line segments to a similar curve with fewer points.

Gnome sort (nicknamed stupid sort) is a variation of the insertion sort sorting algorithm that does not use nested loops.

beam search is a heuristic search algorithm that explores a graph by expanding the most promising node in a limited set.

Suurballe's algorithm is an algorithm for finding two disjoint paths in a nonnegatively-weighted directed graph, so that both paths connect the same pair of vertices and have minimum total length.

Stoer-Wagner algorithm is a recursive algorithm to solve the minimum cut problem in undirected weighted graphs with non-negative weights.

Pollard's rho algorithm is an algorithm for integer factorization.

AKS primality test (also known as the Agrawal-Kayal-Saxena primality test and the cyclotomic AKS test) is a deterministic primality-proving algorithm created and published by Manindra Agrawal, Neeraj Kayal, and Nitin Saxena, computer scientists at the Indian I

CORDIC, short for coordinate rotation digital computer, is a simple and efficient algorithm to calculate trigonometric functions, hyperbolic functions, square roots, multiplications, divisions, exponentials, and logarithms with arbitrary base, typically conver

Metropolis-Hastings algorithm is a Markov chain Monte Carlo (MCMC) method for obtaining a sequence of random samples from a probability distribution from which direct sampling is difficult.

Frank-Wolfe algorithm is an iterative first-order optimization algorithm for constrained convex optimization.

Liang-Barsky algorithm (named after You-Dong Liang and Brian A. Barsky) is a line clipping algorithm first published in early 1984. The Liang-Barsky algorithm uses the parametric equation of a line and inequalities describing the range of the clipping window t

Needleman-Wunsch algorithm is an algorithm used in bioinformatics to align protein or nucleotide sequences.

Smith-Waterman algorithm performs local sequence alignment; that is, for determining similar regions between two strings of nucleic acid sequences or protein sequences.

Edmonds' algorithm or Chu-Liu/Edmonds' algorithm is an algorithm for finding a spanning arborescence of minimum weight (sometimes called an optimum branching).

Gram-Schmidt process or Gram-Schmidt algorithm is a way of finding a set of two or more vectors that are perpendicular to each other.

Toom-Cook, sometimes known as Toom-3, named after Andrei Toom, who introduced the new algorithm with its low complexity, and Stephen Cook, who cleaned the description of it, is a multiplication algorithm for large integers.

Boyer-Moore-Horspool algorithm or Horspool's algorithm is an algorithm for finding substrings in strings.

Earley parser is an algorithm for parsing strings that belong to a given context-free language.

shunting yard algorithm is a method for parsing arithmetical or logical expressions, or a combination of both, specified in infix notation.

Gilbert-Johnson-Keerthi distance algorithm is a method of determining the minimum distance between two convex sets, first published by Elmer G. Gilbert, Daniel W. Johnson, and S. Sathiya Keerthi in 1988. Unlike many other distance algorithms, it does not requi

Hyperlink-Induced Topic Search (HITS; also known as hubs and authorities) is a link analysis algorithm that rates Web pages, developed by Jon Kleinberg.

bitap algorithm (also known as the shift-or, shift-and or Baeza-Yates-Gonnet algorithm) is an approximate string matching algorithm.

GLR parser (generalized left-to-right rightmost derivation parser) is an extension of an LR parser algorithm to handle non-deterministic and ambiguous grammars.

Gale-Shapley algorithm (also known as the deferred acceptance algorithm, propose-and-reject algorithm, or Boston Pool algorithm) is an algorithm for finding a solution to the stable matching problem.

Leiden algorithm is a community detection algorithm developed by Traag et al at Leiden University.

sieve of Atkin is a modern algorithm for finding all prime numbers up to a specified integer.

Pohlig-Hellman algorithm, sometimes credited as the Silver-Pohlig-Hellman algorithm, is a special-purpose algorithm for computing discrete logarithms in a finite abelian group whose order is a smooth integer.

Library sort or gapped insertion sort is a sorting algorithm that uses an insertion sort, but with gaps in the array to accelerate subsequent insertions.

Spreadsort is a sorting algorithm invented by Steven J. Ross in 2002. It combines concepts from distribution-based sorts, such as radix sort and bucket sort, with partitioning concepts from comparison sorts such as quicksort and mergesort.

Flashsort is a distribution sorting algorithm showing linear computational complexity O(n) for uniformly distributed data sets and relatively little additional memory requirement.

Strand sort is a recursive sorting algorithm that sorts items of a list into increasing order.

Tournament sort is a sorting algorithm.

Lloyd's algorithm, also known as Voronoi iteration or relaxation, is an algorithm named after Stuart P. Lloyd for finding evenly spaced sets of points in subsets of Euclidean spaces and partitions of these subsets into well-shaped and uniformly sized convex ce

reverse-delete algorithm is an algorithm in graph theory used to obtain a minimum spanning tree from a given connected, edge-weighted graph.

It is notable for being rapidly convergent, with only 25 iterations producing 45 million correct digits of π. However, it has some drawbacks (for example, it is computer memory-intensive) and therefore all record-breaking calculations for many years have used other methods, almost always the Chudnovsky algorithm.

The Chudnovsky algorithm is a fast method for calculating the digits of π, based on Ramanujan's π formulae.

bogosort (also known as permutation sort and stupid sort) is a sorting algorithm based on the generate and test paradigm.

Bead sort, also called gravity sort, is a natural sorting algorithm, developed by Joshua J. Arulanandham, Cristian S. Calude and Michael J. Dinneen in 2002, and published in The Bulletin of the European Association for Theoretical Computer Science.

Block sort, or block merge sort, is a sorting algorithm combining at least two merge operations with an insertion sort to arrive at O(n log n) (see Big O notation) in-place stable sorting time.

quickselect is a selection algorithm to find the kth smallest element in an unordered list, also known as the kth order statistic.

B* (pronounced "B star") is a best-first graph search algorithm that finds the least-cost path from a given initial node to any goal node (out of one or more possible goals).

blossom algorithm is an algorithm for constructing maximum matchings on graphs.

Fisher-Yates shuffle is an algorithm for shuffling a finite sequence.

Heap's algorithm generates all possible permutations of n objects.

shoelace formula, also known as Gauss's area formula and the surveyor's formula, is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane.

Hirschberg's algorithm, named after its inventor, Dan Hirschberg, is a dynamic programming algorithm that finds the optimal sequence alignment between two strings.

binary search, also known as half-interval search, logarithmic search, or binary chop, is a search algorithm that finds the position of a target value within a sorted array.

The Rete algorithm ( REE-tee, RAY-tee, rarely REET, reh-TAY) is a pattern matching algorithm for implementing rule-based systems.

Maze generation algorithms are automated methods for the creation of mazes.

exclusive or swap (sometimes shortened to XOR swap) is an algorithm that uses the exclusive or bitwise operation to swap the values of two variables without using the temporary variable which is normally required.

polynomial-time approximation scheme (PTAS) is a type of approximation algorithm for optimization problems (most often, NP-hard optimization problems).

Pollard's kangaroo algorithm (also Pollard's lambda algorithm, see Naming below) is an algorithm for solving the discrete logarithm problem.

Kernighan-Lin algorithm is a heuristic algorithm for finding partitions of graphs.

multiplicative weights update method is an algorithmic technique most commonly used for decision making and prediction, and also widely deployed in game theory and algorithm design.

Flajolet-Martin algorithm is an algorithm for approximating the number of distinct elements in a stream with a single pass and space-consumption logarithmic in the maximal number of possible distinct elements in the stream (the count-distinct problem).

greedy algorithm is an algorithm which, at each step, makes the choice that is locally optimal, and subsequently does not reconsider past choices.

automatic differentiation (auto-differentiation, autodiff, or AD), also called algorithmic differentiation, computational differentiation, and differentiation arithmetic is a set of techniques to evaluate the partial derivative of a function specified by a com

Kabsch algorithm, also known as the Kabsch-Umeyama algorithm, named after Wolfgang Kabsch and Shinji Umeyama, is a method for calculating the optimal rotation matrix that minimizes the RMSD (root mean squared deviation) between two paired sets of points.

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.

March algorithm is a widely used algorithm that tests SRAM memory by filling all its entries test patterns.

alpha max plus beta min algorithm is a high-speed approximation of the square root of the sum of two squares.

sieve of Pritchard is an algorithm for finding all prime numbers up to a specified bound.

SMAWK algorithm is an algorithm for finding the minimum value in each row of an implicitly defined totally monotone matrix.

Sardinas-Patterson algorithm is a classical algorithm for determining in polynomial time whether a given variable-length code is uniquely decodable, named after August Albert Sardinas and George W. Patterson, who published it in 1953. The algorithm carries out

Garsia-Wachs algorithm is an efficient method for computers to construct optimal binary search trees and alphabetic Huffman codes, in linearithmic time.

holographic algorithm is an algorithm that uses a holographic reduction.

Kleene's algorithm transforms a given nondeterministic finite automaton (NFA) into a regular expression.

devex algorithm is a pivot rule for the simplex method developed by Paula M. J. Harris.

Lemke-Howson algorithm is an algorithm that computes a Nash equilibrium of a bimatrix game, named after its inventors, Carlton E. Lemke and J. T. Howson.

Z curve (or Z-curve) method is a bioinformatics algorithm for genome analysis.

Karloff-Zwick algorithm, in computational complexity theory, is a randomised approximation algorithm taking an instance of MAX-3SAT Boolean satisfiability problem as input.

Pfaffian orientation of an undirected graph assigns a direction to each edge, so that certain cycles (the "even central cycles") have an odd number of edges in each direction.

randomized rounding is a widely used approach for designing and analyzing approximation algorithms.

behavior selection algorithm, or action selection algorithm, is an algorithm that selects appropriate behaviors or actions for one or more intelligent agents.

Knuth-Eve algorithm is an algorithm for polynomial evaluation.

block swap algorithms swap two regions of elements of an array.

Chandy-Misra-Haas algorithm resource model checks for deadlock in a distributed system.

Boltzmann sampler is an algorithm intended for random sampling of combinatorial structures.

Snap rounding is a method of approximating line segment locations by creating a grid and placing each point in the centre of a cell (pixel) of the grid.

Newest Vertex Bisection is an algorithmic method to locally refine triangulations.

Jump-and-Walk is an algorithm for point location in triangulations (though most of the theoretical analysis were performed in 2D and 3D random Delaunay triangulations).

Swendsen-Wang algorithm is the first non-local or cluster algorithm for Monte Carlo simulation for large systems near criticality.

method of conditional probabilities is a systematic method for converting non-constructive probabilistic existence proofs into efficient deterministic algorithms that explicitly construct the desired object.

Pointer jumping or path doubling is a design technique for parallel algorithms that operate on pointer structures, such as linked lists and directed graphs.

Domain reduction algorithms are algorithms used to reduce constraints and degrees of freedom in order to provide solutions for partial differential equations.

Miller's recurrence algorithm is a procedure for the backward calculation of a rapidly decreasing solution of a three-term recurrence relation developed by J. C. P. Miller.

British Museum algorithm is a general approach to finding a solution by checking all possibilities one by one, beginning with the smallest.

Rao-Sandelius shuffle is a divide-and-conquer algorithm for shuffling a finite sequence.

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.

fully polynomial-time approximation scheme (FPTAS) is an algorithm for finding approximate solutions to function problems, especially optimization problems.

elimination theory is the classical name for algorithmic approaches to eliminating some variables between polynomials of several variables, in order to solve systems of polynomial equations.

APX (an abbreviation of "approximable") is the set of NP optimization problems that allow polynomial-time approximation algorithms with approximation ratio bounded by a constant (or constant-factor approximation algorithms for short).

parameterized approximation algorithm is a type of algorithm that aims to find approximate solutions to NP-hard optimization problems in polynomial time in the input size and a function of a specific parameter.

In mathematics, the Robinson-Schensted-Knuth correspondence, also referred to as the RSK correspondence or RSK algorithm, is a combinatorial bijection between matrices A with non-negative integer entries and pairs (P,Q) of semistandard Young tableaux of equal shape, whose size equals the sum of the entries of A.

Collective operations are building blocks for interaction patterns, that are often used in SPMD algorithms in the parallel programming context.

generalized distributive law (GDL) is a generalization of the distributive property which gives rise to a general message passing algorithm.

Ramesh Sitaraman is an Indian American computer scientist known for his work on distributed algorithms, content delivery networks, streaming video delivery, and application delivery networks.

Martin Farach-Colton is an American computer scientist, known for his work in streaming algorithms, suffix tree construction, pattern matching in compressed data, cache-oblivious algorithms, and lowest common ancestor data structures.

Oscar H. Ibarra (born September 29, 1941 in Negros Occidental, Philippines) is a Filipino-American theoretical computer scientist, prominent for work in automata theory, formal languages, design and analysis of algorithms and computational complexity theory.

Elias Koutsoupias is a Greek computer scientist working in algorithmic game theory.

Multidimensional scaling Kruskal's algorithm Kruskal's tree theorem Kruskal-Katona theorem

Blackman-Tukey transformation Cooley-Tukey FFT algorithm

smoothed analysis of algorithms

He is considered to be the father of computational geometry in Canada.

His research specialty is in the design and analysis of algorithms for graph drawing, computational geometry, and computer security.

His main areas of research are high performance computing, data science, bioinformatics and systems biology, combinatorial methods in scientific computing, and string algorithms.

Inventing commodity supercomputing Scalable Graph Algorithms Founding the School of Computational Science and Engineering at Georgia Tech Founding director, Institute for Data Science at NJIT

Contributions to algorithms and game theory in the context of computer science

John Wilder Tukey (; June 16, 1915, July 26, 2000) was an American mathematician and statistician, best known for the development of the fast Fourier Transform (FFT) algorithm, the box plot and for laying the foundations of the field of exploratory data analysis.

Graham's scan is a method of finding the convex hull of a finite set of points in the plane with time complexity O(n log n).

In computing, a Bloom filter is a space-efficient probabilistic data structure, conceived by Burton Howard Bloom in 1970, that is used to test whether an element is a member of a set.

Cuckoo hashing is a scheme in computer programming for resolving hash collisions of values of hash functions in a table, with worst-case constant lookup time.

Powersort is an adaptive sorting algorithm designed to optimally exploit existing order in the input data with minimal overhead.

A tree sort is a sort algorithm that builds a binary search tree from the elements to be sorted, and then traverses the tree (in-order) so that the elements come out in sorted order.

A quotient filter is a space-efficient probabilistic data structure used to test whether an element is a member of a set (an approximate membership query filter, AMQ). A query will elicit a reply specifying either that the element is definitely not in the set or that the element is probably in the set.

Stooge sort is a recursive sorting algorithm.

In computer science, the Boyer-Moore string-search algorithm is an efficient string-searching algorithm that is the standard benchmark for practical string-search literature.

He was a recipient of the 1998 Gödel Prize for proving Toda's theorem in computational complexity theory, which states that every problem in the polynomial hierarchy has a polynomial-time Turing reduction to a counting problem.

In mathematical optimization, the push-relabel algorithm (alternatively, preflow-push algorithm) is an algorithm for computing maximum flows in a flow network.

It is a non-deterministic algorithm in the sense that it produces a reasonable result only with a certain probability, with this probability increasing as more iterations are allowed.

He is known for his contributions to parallel algorithms in numerical linear algebra.

Metaphone is a phonetic algorithm, published by Lawrence Philips in 1990, for indexing words by their English pronunciation.

The sequence for a tree on n vertices has length n − 2, and can be generated by a simple iterative algorithm.

The Canny edge detector is an edge detection operator that uses a multi-stage algorithm to detect a wide range of edges in images.

In computing, byte-pair encoding (BPE), or digram coding, is an algorithm, first described in 1994 by Philip Gage, for encoding strings of text into smaller strings by creating and using a translation table.

In arithmetic, long division is a standard division algorithm suitable for dividing multi-digit numbers that is simple enough to perform by hand.

The Verhoeff algorithm is a checksum for error detection first published by Dutch mathematician Jacobus Verhoeff in 1969.

The Pan-Tompkins algorithm is commonly used to detect QRS complexes in electrocardiographic signals (ECG).

The Luhn algorithm or Luhn formula (creator: IBM scientist Hans Peter Luhn), also known as the "modulus 10" or "mod 10" algorithm, is a simple check digit formula used to validate a variety of identification numbers.

Zeller's congruence is an algorithm devised by Christian Zeller in the 19th century to calculate the day of the week for any Julian or Gregorian calendar date.

Adler-32 is a checksum algorithm written by Mark Adler in 1995, modifying Fletcher's checksum.

In error detection, the Damm algorithm is a check digit algorithm that detects all single-digit errors and all adjacent transposition errors.

Note G is a computer algorithm traditionally attributed to Ada Lovelace that was designed to calculate Bernoulli numbers using the hypothetical analytical engine designed by Charles Babbage.

In number theory, Berlekamp's root finding algorithm, also called the Berlekamp-Rabin algorithm, is the probabilistic method of finding roots of polynomials over the field F p {\displaystyle \mathbb {F} _{p}} with p {\displaystyle p} elements.

The Manhattan address algorithm is a series of formulas used to estimate the closest east-west cross street for building numbers on north-south avenues in the New York City borough of Manhattan.

The BSD checksum algorithm was a commonly used, legacy checksum algorithm.

More formally, a PIT algorithm is given an arithmetic circuit that computes a polynomial p in a field, and decides whether p is the zero polynomial.

Xulvi-Brunet and Sokolov's algorithm generates networks with chosen degree correlations.

In numerical linear algebra, the Bartels-Stewart algorithm is used to numerically solve the Sylvester matrix equation A X − X B = C {\displaystyle AX-XB=C} .

In multi-armed bandit problems, KL-UCB (for Kullback-Leibler Upper Confidence Bound) is a UCB-type algorithm that is asymptotically optimal, in the sense that its regret matches the problem-dependent Lai-Robbins lower bound.

Collaborative Diffusion is a type of pathfinding algorithm which uses the concept of antiobjects, objects within a computer program that function opposite to what would be conventionally expected.

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.

Bürgi's Kunstweg is a set of algorithms developed by Jost Bürgi in the late 16th century.

The algorithm is used by the Google Crawler to find near duplicate pages.

A hybrid algorithm is an algorithm that combines two or more other algorithms that solve the same problem, either choosing one based on some characteristic of the data, or switching between them over the course of the algorithm.

Communication-avoiding algorithms minimize movement of data within a memory hierarchy for improving its running-time and energy consumption.

The Geohash-36 geocode is an open-source compression algorithm for world coordinate data.

In mathematics, the regula falsi, method of false position, or false position method is a family of algorithms used to solve linear equations and smooth nonlinear equations for a single unknown value.

In mathematics, power iteration (also known as the power method) is an eigenvalue algorithm: given a diagonalizable matrix A {\displaystyle A} , the algorithm will produce a number λ {\displaystyle \lambda } , which is the greatest (in absolute value) eigenvalue of A {\displaystyle A} , and a nonzero vector v {\displaystyle v} , which is a corresponding eigenvector of λ {\displaystyle \lambda } , that is, A v = λ v {\displaystyle Av=\lambda v} .

Trial division is the most laborious but easiest to understand of the integer factorization algorithms.

The Lanczos algorithm is an iterative method devised by Cornelius Lanczos that is an adaptation of power methods to find the m {\displaystyle m} "most useful" (tending towards extreme highest/lowest) eigenvalues and eigenvectors of an n × n {\displaystyle n\times n} Hermitian matrix, where m {\displaystyle m} is often but not necessarily much smaller than n {\displaystyle n} .

It is an iterative algorithm that starts with an arbitrary solution to a problem, then attempts to find a better solution by making an incremental change to the solution.

In anomaly detection, the local outlier factor (LOF) is an algorithm proposed by Markus M.

The quadratic sieve algorithm (QS) is an integer factorization algorithm and, in practice, the second-fastest method known (after the general number field sieve).

In computing, Deflate (stylized as DEFLATE) is a lossless data compression algorithm that uses a combination of LZ77 and Huffman coding.

In number theory, the general number field sieve (GNFS) is the most efficient classical algorithm known for factoring integers larger than 10100.

The process of finding or using such a code is Huffman coding, an algorithm developed by David A.

LZMA (Lempel-Ziv-Markov chain algorithm) is a lossless data compression algorithm developed since 1998 by Igor Pavlov, the developer of 7-Zip.

In computer science, a red-black tree is a self-balancing binary search tree data structure noted for fast storage and retrieval of ordered information.

In statistics and control theory, Kalman filtering (also known as linear quadratic estimation) is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, to produce estimates of unknown variables that tend to be more accurate than those based on a single measurement, by estimating a joint probability distribution over the variables for each time-step.

In statistics, Gibbs sampling or a Gibbs sampler, also known in statistical mechanics as the heat bath algorithm, is a Markov chain Monte Carlo (MCMC) algorithm for sampling from a specified multivariate probability distribution when direct sampling from the joint distribution is difficult, but sampling from the conditional distribution is more practical.

The most commonly used version of the Mersenne Twister algorithm is based on the Mersenne prime 2 19937 − 1 {\displaystyle 2^{19937}-1} .

Zstandard is a lossless data compression algorithm developed by Yann Collet at Facebook.

PPM algorithms can also be used to cluster data into predicted groupings in cluster analysis.

Grey Wolf Optimization (GWO) is a nature-inspired metaheuristic algorithm that mimics the leadership hierarchy and hunting behavior of grey wolves in the wild.

He is known for his research on the graph isomorphism problem and on algorithms for computational group theory.

His research focuses on computational complexity theory, algorithms, combinatorics, and finite groups, with an emphasis on the interactions between these fields.

He is known for his research in computational complexity theory and algorithmic game theory.

He was most famous for his ellipsoid algorithm (1979) for linear programming, which was the first such algorithm known to have a polynomial running time.

Esko Juhani Ukkonen (born 1950) is a Finnish theoretical computer scientist known for his contributions to string algorithms, and particularly for Ukkonen's algorithm for suffix tree construction.

His research interests include the design and analysis of algorithms, computational complexity and cryptography.

Johan Torkel Håstad (Swedish pronunciation: [ˈjûːan ˈhǒːsta]; born 19 November 1960) is a Swedish theoretical computer scientist most known for his work on computational complexity theory.

Szegedy's research areas include computational complexity theory, quantum computing, computational geometry, and computational theory.

His work has mainly focused on efficient algorithms for problems of a mathematical (often geometric) flavor that arise in Computer Science, Machine Learning and Optimization.

Mark N. Wegman is an American computer scientist known for his contributions to algorithms and compiler optimization.