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Algorithm for graph coloring
The Recursive Largest First (RLF) algorithm is a heuristic for the NP-hard graph coloring problem. It was originally proposed by Frank Leighton in 1979
Recursive largest first algorithm
Recursive_largest_first_algorithm
Methodic assignment of colors to elements of a graph
graph colouring are the DSatur and recursive largest first (RLF) algorithms. Similarly to the greedy colouring algorithm, DSatur colours the vertices of
Graph_coloring
Graph colouring algorithm by Daniel Brélaz
in turn producing significantly worse colourings than the recursive largest first algorithm. Brélaz, Daniel (1979-04-01). "New methods to color the vertices
DSatur
Sequence of operations for a task
have export restrictions (see export of cryptography). Recursion A recursive algorithm invokes itself repeatedly until meeting a termination condition and
Algorithm
Method for finding kth smallest value
value is in L {\displaystyle L} , and can be found recursively by applying the same selection algorithm to L {\displaystyle L} . If k = | L | + 1 {\displaystyle
Selection_algorithm
Mathematical puzzle game
tower. This provides the following algorithm, which is easier, carried out by hand, than the recursive algorithm. In alternate moves: Move the smallest
Tower_of_Hanoi
Node ordering for directed acyclic graphs
the algorithm runs in linear time. This depth-first-search-based algorithm is the one described by Cormen et al. (2001); it seems to have been first described
Topological_sorting
Subset of artificial intelligence
intelligence concerned with the development and study of statistical algorithms that can learn from data and generalize to unseen data, and thus perform
Machine_learning
Algorithm that arranges lists in order
is considered "in-place". Recursion: Some algorithms are either typically recursive or typically non-recursive, while others may typically be both (e.g
Sorting_algorithm
Check the validity of a logic formula
Since the set of valid first-order formulas is recursively enumerable but not recursive, there exists no general algorithm to solve this problem. Therefore
Davis–Putnam_algorithm
Divide and conquer sorting algorithm
the recursive calls. The algorithms make exactly the same comparisons, but in a different order. An often desirable property of a sorting algorithm is
Quicksort
Mathematical logic concept
(c.e.), recursively enumerable (r.e.), semidecidable, partially decidable, listable, provable or Turing-recognizable if: There is an algorithm such that
Computably_enumerable_set
Artificial intelligence model developed by TypeSafe AI
BERT-like architecture. Jev is trained exclusively on synthetic data, by an algorithm the company calls Reinforcement Learning for Calibrated Decisions (RLCD)
Jev_(AI_model)
Algorithm for shuffling a finite sequence
algorithm that divides the array into blocks of roughly equal size, uses Fisher–Yates to shuffle each block, and then uses a random merge recursively
Fisher–Yates_shuffle
to half the size of the original problem. This is done recursively, resulting in an algorithm that takes about twice as long but requires only linear
Package-merge_algorithm
Algorithm for fast exponentiation
to be compared with the trivial algorithm which requires n − 1 multiplications. This algorithm is not tail-recursive. This implies that it requires an
Exponentiation_by_squaring
Discrete Fourier transform algorithm
idea is recursive, most traditional implementations rearrange the algorithm to avoid explicit recursion. Also, because the Cooley–Tukey algorithm breaks
Fast_Fourier_transform
matching wildcards algorithm: an open-source non-recursive algorithm Rich Salz' wildmat: a widely used open-source recursive algorithm Substring search
List_of_algorithms
Sorting algorithm
elements to the right to clear a spot for x = A[i]. The algorithm can also be implemented in a recursive way. The recursion just replaces the outer loop, calling
Insertion_sort
Algorithm for computing greatest common divisors
Euclidean algorithm, or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers, the largest number that
Euclidean_algorithm
Limitative results in mathematical logic
The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e. an algorithm) is
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Combinatorial algorithm
algorithm has a natural recursive structure, that can be generated by a recursive algorithm. However the actual Steinhaus–Johnson–Trotter algorithm does
Steinhaus–Johnson–Trotter algorithm
Steinhaus–Johnson–Trotter_algorithm
Type of search algorithm
basic backtracking algorithm runs by choosing a literal, assigning a truth value to it, simplifying the formula and then recursively checking if the simplified
DPLL_algorithm
Algorithm for computing the greatest common divisor
The binary GCD algorithm, also known as Stein's algorithm or the binary Euclidean algorithm, is an algorithm that computes the greatest common divisor
Binary_GCD_algorithm
Method for division with remainder
A division algorithm is an algorithm which, given two integers N and D (respectively the numerator and the denominator), computes their quotient and/or
Division_algorithm
Decision rule used for minimizing the possible loss for a worst-case scenario
(i.e., to maximize B's own chances of winning). A minimax algorithm is a recursive algorithm for choosing the next move in an n-player game, usually a
Minimax
Rooted binary tree data structure
pseudocode implements the BST search procedure through recursion. The recursive procedure continues until a nil {\displaystyle {\text{nil}}} or the key
Binary_search_tree
Algorithm in graph theory
Floyd–Warshall algorithm (also known as Floyd's algorithm, the Roy–Warshall algorithm, the Roy–Floyd algorithm, or the WFI algorithm) is an algorithm for finding
Floyd–Warshall_algorithm
Concept in computability theory
exists, then every algorithm for B {\displaystyle B} can be used to produce an algorithm for A {\displaystyle A} , by inserting the algorithm for B {\displaystyle
Turing_reduction
Thesis on the nature of computability
computability theory, discussed above. The argument that super-recursive algorithms are indeed algorithms in the sense of the Church–Turing thesis has not found
Church–Turing_thesis
Algorithm for solving systems of linear equations
mathematics, Gaussian elimination, also known as row reduction, is an algorithm for solving systems of linear equations. It consists of a sequence of
Gaussian_elimination
Field of machine learning
unsupervised learning. While supervised learning and unsupervised learning algorithms respectively attempt to discover patterns in labeled and unlabeled data
Reinforcement_learning
Technique for finding an extremum of a function
but very robust. The technique derives its name from the fact that the algorithm maintains the function values for four points whose three interval widths
Golden-section_search
Sorting algorithm using the heap data structure
this can be used as a primitive in an in-place (and non-recursive) "QuickHeapsort" algorithm. First, you perform a quicksort-like partitioning pass, but
Heapsort
Computing the fixed point of a function
the iteration algorithm when L {\displaystyle L} is close to 1. The algorithm is recursive: it handles a d-dimensional function by recursive calls on (d-1)-dimensional
Fixed-point_computation
symbols, but may allow negated predicates; recursive concepts are also learnable. Like the ID3 algorithm, FOIL hill climbs using a metric based on information
First-order_inductive_learner
S2CID 63854223. Korf, Richard E. (2011-07-16). "A hybrid recursive multi-way number partitioning algorithm". Proceedings of the Twenty-Second International Joint
Multiway_number_partitioning
Computer data structure
endif else if h[m] > h[i] then: swap h[m] and h[i] endif endif As the recursive calls in push-down-min and push-down-max are in tail position, these functions
Min-max_heap
Sorting algorithm
than 10–20 elements). A useful optimization in practice for the recursive algorithms is to switch to insertion sort or selection sort for "small enough"
Selection_sort
Concept in computational geometry
such subset, recursively compute the MDS of Cleft and the MDS of Cright, and return the largest combined set. The run time of this algorithm satisfies the
Maximum_disjoint_set
Relaxed variant of the sorting problem
specialized partial sorting algorithms based on mergesort and quicksort. In the quicksort variant, there is no need to recursively sort partitions which only
Partial_sorting
Greatest integer less than or equal to square root
being logical right shift, a recursive algorithm to find the integer square root of any natural number is: def isqrt_recursive(n: int) -> int: assert n >=
Integer_square_root
Process of producing small rectangular items of fixed dimensions
height hi+hj. Every pattern can be represented as a recursive sequence of builds. Every recursive sequence of builds corresponds to many different patterns
Guillotine_cutting
Task of computing complete subgraphs
listed by the Bron–Kerbosch algorithm, a recursive backtracking procedure of Bron & Kerbosch (1973). The main recursive subroutine of this procedure
Clique_problem
Computational task of sorting whole numbers
largest possible key to be sorted, and the number w of bits that can be represented in a single machine word of the computer on which the algorithm is
Integer_sorting
Machine learning framework for portfolio construction
clusters inversely proportional to their estimated variances. The recursive algorithm proceeds as follows: Initialize a list L with all asset indices:
Hierarchical_Risk_Parity
Problem in combinatorial optimization
up to i {\displaystyle i} (first i {\displaystyle i} items). We can define m [ i , w ] {\displaystyle m[i,w]} recursively as follows: (Definition A) m
Knapsack_problem
Sorting algorithm in computer science
original algorithm until the sorting is completed. To avoid stack overflow caused by recursion, use a Boolean data type tag array to operate the recursive function
Interpolation_sort
Image edge detection algorithm
Canny edge detector is an edge detection operator that uses a multi-stage algorithm to detect a wide range of edges in images. It was developed by John F
Canny_edge_detector
Non-comparative lexicographical sorting algorithm
stable, in-place, and can significantly speed up radix sort. This recursive sorting algorithm has particular application to parallel computing, as each of
Radix_sort
Type of hash function
A rolling hash (also known as recursive hashing or rolling checksum) is a hash function where the input is hashed in a window that moves through the input
Rolling_hash
Search engine from Google
phrases on a website page or in an installed application program. It uses algorithms to analyze and rank websites based on their relevance to the query and
Google_Search
Subfield of mathematical optimization
(a recursive solution construction with limited search window) and tabu search (a greedy-type swapping algorithm). However, generic search algorithms are
Combinatorial_optimization
Algorithmic runtime requirements for matrix multiplication
subproblems of multiplying two n/2×n/2 matrices. Applying this recursively gives an algorithm needing O ( n log 2 7 ) ≈ O ( n 2.807 ) {\displaystyle O(n^{\log
Computational complexity of matrix multiplication
Computational_complexity_of_matrix_multiplication
Set of objects whose state must satisfy limits
consistency, a recursive call is performed. When all values have been tried, the algorithm backtracks. In this basic backtracking algorithm, consistency
Constraint satisfaction problem
Constraint_satisfaction_problem
Data structure for a string
Puglisi, Smyth & Turpin (2007). A well-known recursive algorithm for integer alphabets is the DC3 / skew algorithm of Kärkkäinen & Sanders (2003). It runs
Suffix_array
Succinct data structure
assignment. For instance, "largest ← item" means that the value of largest changes to the value of item. "return" terminates the algorithm and outputs the following
Wavelet_Tree
Scientific area at the interface between computer science and mathematics
computation, is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions and other mathematical
Computer_algebra
Complexity measure in computer science
is the recursive copy (i.e., the shallow copy). The underlying mechanism in this complexity measure is the starting point for some algorithms for lossless
Lempel–Ziv_complexity
Variation of the classical Tower of Hanoi puzzle
most instructive methods for solving the MToH is to use recursive algorithms. Such algorithms are presented below for selected variations of the puzzle
Magnetic_Tower_of_Hanoi
Efficient sorting algorithm that combines insert and merge operations
merge algorithm divides A into discrete blocks of size √A (resulting in √A number of blocks as well), inserts each A block into B such that the first value
Block_sort
Self-balancing binary search tree
and B, is a weight-balanced tree t that represents A ∪ B. The following recursive function computes this union: function union(t1, t2): if t1 = nil: return
Weight-balanced_tree
Sequence of integers
greedy algorithm for finding a representation of n {\displaystyle n} as a sum of primes: choose the first prime in the sum to be the largest prime p
Pillai_sequence
Intelligence in machines
attention and cover the scope of AI research. Early researchers developed algorithms that imitated step-by-step reasoning that humans use when solving puzzles
Artificial_intelligence
System with self-optimizing transfer function
parameters according to an optimization algorithm. Because of the complexity of the optimization algorithms, almost all adaptive filters are digital
Adaptive_filter
and conquer algorithm An algorithm design paradigm based on multi-branched recursion. A divide-and-conquer algorithm works by recursively breaking down
Glossary_of_computer_science
Orthonormalization of a set of vectors
Gram-Schmidt is computationally (exponentially) slower than the recursive algorithms described above; it is mainly of theoretical interest. Expressed
Gram–Schmidt_process
Finite-state machine
NP-complete. The first algorithm for minimal DFA identification has been proposed by Trakhtenbrot and Barzdin and is called the TB-algorithm. However, the
Deterministic finite automaton
Deterministic_finite_automaton
Theoretical description of Earth's gravimetric shape
i.e. the gradient of the potential, must be computed. Efficient recursive algorithms have been designed to compute the gravitational force for any N z
Geopotential spherical harmonic model
Geopotential_spherical_harmonic_model
Product of numbers from 1 to n
conquer and another coming from the multiplication algorithm. In the recursive calls to the algorithm, the prime number theorem can again be invoked to
Factorial
Mathematics problem
simplest pancake sorting algorithm performs at most 2n − 3 flips. In this algorithm, a kind of selection sort, we bring the largest pancake not yet sorted
Pancake_sorting
Methods to test or prove primality
primality of q. This is verified using the same algorithm. So we have described a recursive algorithm, where the primality of N depends on the primality
Elliptic_curve_primality
Theories in mathematical logic
axiomatizable; be decidable: There is an algorithm to decide which statements are provable; be recursively axiomatizable; be model complete or sub-model
List_of_first-order_theories
Measure of algorithmic complexity
In algorithmic information theory (a subfield of computer science and mathematics), the Kolmogorov complexity of an object, such as a piece of text, is
Kolmogorov_complexity
One-by-one assignment of colors to graph vertices
subgraph with v removed recursively, and then place v last in the ordering. The largest degree of a removed vertex that this algorithm encounters is called
Greedy_coloring
Least-weight tree connecting graph vertices
the starting graph. Apply the optimal algorithm recursively to this graph. The runtime of all steps in the algorithm is O(m), except for the step of using
Minimum_spanning_tree
the two that calls the iterative algorithm from the recursive algorithm. The recursive algorithm repeatedly chooses random samples whose size is approximately
LP-type_problem
Variant of heap data structure
smallest or largest element from (respectively) a min-heap or max-heap. Binary heaps are also commonly employed in the heapsort sorting algorithm, which is
Binary_heap
Image dithering algorithm
Ordered dithering is any image dithering algorithm which uses a pre-set threshold map tiled across an image. It is commonly used to display a continuous
Ordered_dithering
Binary tree selected at random
Karger–Stein algorithm for finding minimum cuts in graphs, using a recursive edge contraction process. This algorithm calls itself twice recursively, with each
Random_binary_tree
Statistical method in data analysis
data points in a single cluster and recursively splits the cluster into smaller ones. At each step, the algorithm selects a cluster and divides it into
Hierarchical_clustering
Coding theory algorithm
In coding theory, Zemor's algorithm, designed and developed by Gilles Zémor, is a recursive low-complexity approach to code construction. It is an improvement
Zemor's_decoding_algorithm
Comparison-based sorting algorithm
sorting algorithm. A variant of heapsort, it was invented and published by Edsger Dijkstra in 1981. Like heapsort, smoothsort is an in-place algorithm with
Smoothsort
Graph where all long cycles have a chord
graph may be found efficiently using an algorithm known as lexicographic breadth-first search. This algorithm maintains a partition of the vertices of
Chordal_graph
Invariants used to prove properties of loops
loops and recursive programs, proving partial correctness of loops with invariants is very similar to proving the correctness of recursive programs via
Loop_invariant
Algorithm for polynomial evaluation
mathematics and computer science, Horner's method (or Horner's scheme) is an algorithm for polynomial evaluation. It is named after William George Horner, although
Horner's_method
Integer factorization algorithm
most laborious but easiest to understand of the integer factorization algorithms. The essential idea behind trial division tests to see if an integer n
Trial_division
Mathematical problem set on a chessboard
programming or genetic algorithms. Most often, it is used as an example of a problem that can be solved with a recursive algorithm, by phrasing the n queens
Eight_queens_puzzle
Measure of a systems floating point architecture
depths of look-ahead recursive panel factorization six different panel broadcasting variants bandwidth-reducing swap–broadcast algorithm backward substitution
LINPACK_benchmarks
both methods are not suitable as an effective algorithm. The first complete real-root isolation algorithm was given by Jacques Charles François Sturm in
Polynomial_root-finding
Chinese artificial intelligence company
paper in May 2022 introducing the GLM (General Language Model) training algorithm, which uses an "autoregressive blank infilling" strategy that creates
Z.ai
Fractal named after mathematician Benoit Mandelbrot
recursive detail at increasing magnifications; mathematically, the boundary of the Mandelbrot set is a fractal curve. The "style" of this recursive detail
Mandelbrot_set
Algorithm
Head/tail breaks is a clustering algorithm for data with a heavy-tailed distribution such as power laws and lognormal distributions. The heavy-tailed
Head/tail_breaks
Binary tree derived from a sequence of numbers
Cartesian tree construction is based on divide-and-conquer. The algorithm recursively constructs the tree on each half of the input, and then merges the
Cartesian_tree
Large number coined by Ronald Graham
computable recursive formulas using Knuth's up-arrow notation or equivalent, as was done by Ronald Graham, the number's namesake. As there is a recursive formula
Graham's_number
Branch of machine learning
Unfortunately, the learning algorithm was not a functional one, and fell into oblivion. The first working deep learning algorithm was the Group method of
Deep_learning
Concept in integral mathematics
recursively solve subproblems in which some of the fractional variables have their values fixed to either zero or one. In each step of an algorithm of
Linear_programming_relaxation
Describes approximate behavior of a function
this article Master theorem (analysis of algorithms): For analyzing divide-and-conquer recursive algorithms using big O notation Nachbin's theorem: A
Big_O_notation
Sequence of characters that forms a search pattern
match pattern in text. Usually such patterns are used by string-searching algorithms for "find" or "find and replace" operations on strings, or for input validation
Regular_expression
Open problem on 3x+1 and x/2 functions
\\f(a_{i-1})&{\text{for }}i>0\end{cases}}} (that is: ai is the value of f applied to n recursively i times; ai = f i(n)). The Collatz conjecture is: This process will eventually
Collatz_conjecture
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RECURSIVE LARGEST-FIRST-ALGORITHM
RECURSIVE LARGEST-FIRST-ALGORITHM
RECURSIVE LARGEST-FIRST-ALGORITHM
RECURSIVE LARGEST-FIRST-ALGORITHM
RECURSIVE LARGEST-FIRST-ALGORITHM
RECURSIVE LARGEST-FIRST-ALGORITHM
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RECURSIVE LARGEST-FIRST-ALGORITHM
RECURSIVE LARGEST-FIRST-ALGORITHM
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