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Matrix manipulation algorithm
In numerical analysis, the minimum degree algorithm is an algorithm used to permute the rows and columns of a symmetric sparse matrix before applying the
Minimum_degree_algorithm
length in a given graph Minimum spanning tree Borůvka's algorithm Kruskal's algorithm Prim's algorithm Reverse-delete algorithm Nonblocking minimal spanning
List_of_algorithms
Least-weight tree connecting graph vertices
all of the algorithms below, m is the number of edges in the graph and n is the number of vertices. The first algorithm for finding a minimum spanning tree
Minimum_spanning_tree
Algorithm that employs a degree of randomness as part of its logic or procedure
A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random
Randomized_algorithm
Algorithm for finding shortest paths
Dijkstra's algorithm (/ˈdaɪk.strəz/, DYKE-strəz) is an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent
Dijkstra's_algorithm
Approximation for the travelling salesman problem
Then the algorithm can be described in pseudocode as follows. Create a minimum spanning tree T of G. Let O be the set of vertices with odd degree in T. By
Christofides_algorithm
Randomized algorithm for minimum cuts
In computer science and graph theory, Karger's algorithm is a randomized algorithm to compute a minimum cut of a connected graph. It was invented by David
Karger's_algorithm
Graph theory concept
(2007) found a linear time algorithm that can find the minimum degree spanning tree of series-parallel graphs with small degrees. G. Yao, D. Zhu, H. Li,
Minimum_degree_spanning_tree
Matrix decomposition method
Cycle rank Incomplete Cholesky factorization Matrix decomposition Minimum degree algorithm Square root of a matrix Sylvester's law of inertia Symbolic Cholesky
Cholesky_decomposition
Type of spanning tree
^{*}} is the minimum possible maximum degree over all spanning trees. Thus, if k = Δ ∗ {\displaystyle k=\Delta ^{*}} , such an algorithm will either return
Degree-constrained spanning tree
Degree-constrained_spanning_tree
Concept in numerical linear algebra
fill-reducing reorderings of the matrix's unknowns, such as the Minimum degree algorithm. An incomplete factorization instead seeks triangular matrices
Incomplete_LU_factorization
Shortest network connecting points
the Delaunay triangulation and then applying a graph minimum spanning tree algorithm, the minimum spanning tree of n {\displaystyle n} given planar points
Euclidean minimum spanning tree
Euclidean_minimum_spanning_tree
clustering algorithm (also known as the HCS algorithm, and other names such as Highly Connected Clusters/Components/Kernels) is an algorithm based on graph
HCS_clustering_algorithm
decomposition algorithm Block LU decomposition Cholesky decomposition — for solving a system with a positive definite matrix Minimum degree algorithm Symbolic
List of numerical analysis topics
List_of_numerical_analysis_topics
Numerical linear algebra algorithm
numerical linear algebra, the Cuthill–McKee algorithm (CM), named after Elizabeth Cuthill and James McKee, is an algorithm to permute a sparse matrix that has
Cuthill–McKee_algorithm
Point set triangulation minimizing total length
Although NP-hard, the minimum weight triangulation may be constructed in subexponential time by a dynamic programming algorithm that considers all possible
Minimum-weight_triangulation
Class of algorithms that find approximate solutions to optimization problems
polynomial-time algorithm that uses at most one additional color than the minimum needed. A notable example of an approximation algorithm that provides
Approximation_algorithm
Decision rule used for minimizing the possible loss for a worst-case scenario
the values are assigned to each parent node. The algorithm continues evaluating the maximum and minimum values of the child nodes alternately until it reaches
Minimax
Model selection principle
Minimum description length (MDL) is a model selection principle where the shortest description of the data is judged to be the best model. MDL methods
Minimum_description_length
Subset of a graph's vertices, including at least one endpoint of every edge
of finding a minimum vertex cover is a classical optimization problem. It is NP-hard, so it cannot be solved by a polynomial-time algorithm if P ≠ NP. Moreover
Vertex_cover
Vector quantization algorithm minimizing the sum of squared deviations
the original algorithm, including methods such as fuzzy c-means, which allows data points to belong to multiple clusters with varying degrees of membership
K-means_clustering
Cryptographic algorithm created by Adi Shamir
Shamir's secret sharing (SSS) is an efficient secret sharing algorithm for distributing private information (the "secret") among a group, first developed
Shamir's_secret_sharing
Algorithm in graph theory
given degree sequence exists, or proves that one cannot find a positive answer. This construction is based on a recursive algorithm. The algorithm was published
Havel–Hakimi_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
Algorithms for mesh generation
produce a local feature size-graded meshes with minimum angle up to about 28.6 degrees. The algorithm begins with a constrained Delaunay triangulation
Delaunay_refinement
Number of edges touching a vertex in a graph
{\displaystyle G} 's vertices' degrees. The minimum degree of a graph is denoted by δ ( G ) {\displaystyle \delta (G)} , and is the minimum of G {\displaystyle G}
Degree_(graph_theory)
Criterion applied in hierarchical cluster analysis
known as Ward's method or more precisely Ward's minimum variance method. The nearest-neighbor chain algorithm can be used to find the same clustering defined
Ward's_method
Independent set which is not a subset of any other independent set
(whose degree is lower than the degree of v) and higher neighbours (whose degree is higher than the degree of v), breaking ties as in the algorithm. Call
Maximal_independent_set
Unrelated vertices in graphs
degree; for instance, a greedy algorithm that forms a maximal independent set by, at each step, choosing the minimum degree vertex in the graph and removing
Independent set (graph theory)
Independent_set_(graph_theory)
Competitive algorithm for searching a problem space
genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA) in
Genetic_algorithm
Subset of a graph's nodes such that all other nodes link to at least one
S4}. If the graph has maximum degree Δ, then the greedy approximation algorithm finds an O(log Δ)-approximation of a minimum dominating set. Also, let dg
Dominating_set
Abstract data type in computer science
matrix, priority queue can be used to extract minimum efficiently when implementing Dijkstra's algorithm, although one also needs the ability to alter
Priority_queue
Type of clustering of data points
set to 2. The algorithm minimizes intra-cluster variance as well, but has the same problems as 'k'-means; the minimum is a local minimum, and the results
Fuzzy_clustering
Problems in computer science
maximal degree, shortest paths, etc., when insertion and deletion of its edges are allowed. Examples: There is an algorithm that maintains the minimum spanning
Dynamic_problem_(algorithms)
Triangulation method
If the Delaunay triangulation is calculated using the Bowyer–Watson algorithm then the circumcenters of triangles having a common vertex with the "super"
Delaunay_triangulation
French computer scientist (born 1955)
structure and the most asymptotically efficient known deterministic algorithm for finding minimum spanning trees. Chazelle was born in Clamart, France, the son
Bernard_Chazelle
Cycles in a graph that generate all cycles
basis algorithm leads to a polynomial time algorithm for the minimum weight cycle basis. Subsequent researchers have developed improved algorithms for this
Cycle_basis
Basic concept of graph theory
connectivity equals its minimum degree. A graph is said to be maximally edge-connected if its edge-connectivity equals its minimum degree. A graph is said to
Connectivity_(graph_theory)
connected subgraph of vertices with at least degree k. This algorithm can only be applied to unweighted graphs. A minimum spanning tree is a tree-like subgraph
Disparity filter algorithm of weighted network
Disparity_filter_algorithm_of_weighted_network
Vertices whose removal breaks all cycles
the size of a minimum feedback vertex set can be solved in time O(1.7347n), where n is the number of vertices in the graph. This algorithm actually computes
Feedback_vertex_set
Estimate of time taken for running an algorithm
takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that
Time_complexity
Optimization algorithms using quantum computing
Quantum optimization algorithms are quantum algorithms that are used to solve optimization problems. Mathematical optimization deals with finding the
Quantum optimization algorithms
Quantum_optimization_algorithms
On short connecting nets with added points
close to 1 in polynomial time. There is a polynomial-time algorithm that approximates the minimum Steiner tree to within a factor of ln ( 4 ) + ε ≈ 1.386
Steiner_tree_problem
Number of bits in a key used by a cryptographic algorithm
(that is, the algorithm's design does not detract from the degree of security inherent in the key length). Most symmetric-key algorithms are designed to
Key_size
The Lindsey–Fox algorithm, named after Pat Lindsey and Jim Fox, is a numerical algorithm for finding the roots or zeros of a high-degree polynomial with
Lindsey–Fox_algorithm
The Shinnar–Le Roux (SLR) algorithm is a mathematical tool for generating frequency-selective radio frequency (RF) pulses in magnetic resonance imaging
Shinnar–Le_Roux_algorithm
Optimization technique
designed to find, generate, tune, or select a heuristic (partial search algorithm) that may provide a sufficiently good solution to an optimization problem
Metaheuristic
Optimization algorithm
minimum (= with a positive second derivative), then it has quadratic convergence. Regula falsi is another method that fits the function to a degree-two
Line_search
Mathematical and computational problem
produced with sophisticated algorithms. In addition, many approximation algorithms exist. For example, the first fit algorithm provides a fast but often
Bin_packing_problem
2015 password-based key derivation function
version 1.3. The second attack shows that Argon2i can be computed by an algorithm which has complexity O(n7/4 log(n)) for all choices of parameters σ (space
Argon2
Type of spanning tree
between each node and its parent. The above algorithm guarantees the existence of shortest-path trees. Like minimum spanning trees, shortest-path trees in
Shortest-path_tree
Graph divided into two independent sets
Robert (2004), Algorithms in Java, Part 5: Graph Algorithms (3rd ed.), Addison Wesley, pp. 109–111. Kleinberg, Jon; Tardos, Éva (2006), Algorithm Design, Addison
Bipartite_graph
NP-hard problem in combinatorial optimization
algorithm of Christofides and Serdyukov follows a similar outline but combines the minimum spanning tree with a solution of another problem, minimum-weight
Travelling_salesman_problem
Computational problem of graph theory
corresponds to a single move or turn, shortest path algorithms can be used to find a solution that uses the minimum possible number of moves. In a networking or
Shortest_path_problem
Data structure for priority queue operations
asymptotic running time of algorithms which utilize priority queues. For example, Dijkstra's algorithm and Prim's algorithm can be made to run in O ( |
Fibonacci_heap
American computer scientist
Karger's algorithm, a Monte Carlo method to compute the minimum cut of a connected graph. Karger developed the fastest minimum spanning tree algorithm to date
David_Karger
Edges that hit all cycles in a graph
In graph theory and graph algorithms, a feedback arc set or feedback edge set in a directed graph is a subset of the edges of the graph that contains at
Feedback_arc_set
Algorithm for finding zeros of functions
method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes)
Newton's_method
Signal processing method
The Parks–McClellan algorithm, published by James McClellan and Thomas Parks in 1972, is an iterative algorithm for finding the optimal Chebyshev finite
Parks–McClellan filter design algorithm
Parks–McClellan_filter_design_algorithm
Inference algorithm for probabilistic graphical models
Variable elimination (VE) is a simple and general exact inference algorithm in probabilistic graphical models, such as Bayesian networks and Markov random
Variable_elimination
Set of hypergraph nodes to which every hyperedge is connected
finding a minimum d-hitting set permits a d-approximation algorithm. Assuming the unique games conjecture, this is the best constant-factor algorithm that
Vertex_cover_in_hypergraphs
Academic grading structure in the United Kingdom
bachelor's degree takes four years and requires 480 credits with a minimum of 90 at level 10 of the Scottish framework (last year of the honours degree) and
British undergraduate degree classification
British_undergraduate_degree_classification
Data structure for integer priorities
graph, prioritized by their degrees, and repeatedly find and remove the vertex of minimum degree. This greedy algorithm can be used to calculate the
Bucket_queue
Classical problem in combinatorics
factor- log n {\displaystyle \scriptstyle \log n} approximation algorithm for the minimum set cover problem. See setcover for a detailed explanation. The
Set_cover_problem
Simplicial complex in Euclidean geometry
Santos, Francisco (2010). Triangulations, Structures for Algorithms and Applications. Algorithms and Computation in Mathematics. Vol. 25. Springer. de Berg
Point-set_triangulation
Number of forests a graph's edges may be partitioned into
graph is closely related to its maximum degree and its slope number. The pseudoarboricity of a graph is the minimum number of pseudoforests into which its
Arboricity
Algorithm to approximate functions
The Remez algorithm or Remez exchange algorithm, published by Evgeny Yakovlevich Remez in 1934, is an iterative algorithm used to find simple approximations
Remez_algorithm
Concept in graph theory
varying levels of success. One of the oldest algorithms for dividing networks into parts is the minimum cut method (and variants such as ratio cut and
Community_structure
vertices to find the one that induces the connector of minimum Wiener index yields an algorithm that finds the optimum solution in 2 O ( n ) {\displaystyle
Wiener_connector
Algorithm for listing maximal cliques
selecting the vertex of minimum degree among the remaining vertices. If the order of the vertices v that the Bron–Kerbosch algorithm loops through is a degeneracy
Bron–Kerbosch_algorithm
Algorithm to search the nodes of a graph
science, depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures. The algorithm starts at the root node (selecting
Depth-first_search
Methodic assignment of colors to elements of a graph
faster for sufficiently large maximum degree Δ than deterministic algorithms. The fastest randomized algorithms employ the multi-trials technique by Schneider
Graph_coloring
Planar maps require at most five colors
bounded by two edges, and has minimum degree 5. Then G has a vertex of degree 5 which is adjacent to a vertex of degree at most 6. We will use a representation
Five_color_theorem
Tree which includes all vertices of a graph
often use algorithms that gradually build a spanning tree (or many such trees) as intermediate steps in the process of finding the minimum spanning tree
Spanning_tree
Fewest graph edges whose removal breaks all cycles
is possible to construct a minimum-size set of edges that breaks all cycles efficiently, either using a greedy algorithm or by complementing a spanning
Cyclomatic_number
Numerical eigenvalue calculation
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
Lanczos_algorithm
Assignment of colors to edges of a graph
and his algorithm solves the two subproblems recursively. The total time for his algorithm is O(m log m). For planar graphs with maximum degree Δ ≥ 7,
Edge_coloring
tree Trie Patricia trie Spanning tree Minimum spanning tree Boruvka's algorithm Kruskal's algorithm Prim's algorithm Steiner tree Quadtree Node Child node
List_of_graph_theory_topics
Quantum physics-based metaheuristic for optimization problems
annealing-based algorithms and two examples of this kind of algorithms for solving instances of the max-SAT (maximum satisfiable problem) and Minimum Multicut
Quantum_annealing
Mathematics problem
another with the minimum number of prefix reversals is NP-complete. They also gave bounds for the same. Hurkens et al. gave an exact algorithm to sort binary
Pancake_sorting
Maximal biconnected subgraph
decomposition of G. Then G is 2-vertex-connected if and only if G has minimum degree 2 and C1 is the only cycle in C. This gives immediately a linear-time
Biconnected_component
Tree node with two other nodes as descendants
this algorithm is O(h) where h is the height of the tree (length of longest path from a leaf to the root). However, there exist several algorithms for
Lowest_common_ancestor
Machine learning paradigm
supervised learning (SL) is a type of machine learning paradigm where an algorithm learns to map input data to a specific output based on example input-output
Supervised_learning
Polynomial function of degree 4
have another local maximum and another local minimum. The degree four (quartic case) is the highest degree such that every polynomial equation can be solved
Quartic_function
the minimum spanning tree of its input, because the greedy construction algorithm follows the same insertion order of edges as Kruskal's algorithm for
Greedy_geometric_spanner
Method of executing orders
Algorithmic trading is a method of executing orders using automated pre-programmed trading instructions accounting for variables such as time, price,
Algorithmic_trading
Algorithm used for frequency estimation and radio direction finding
MUSIC (MUltiple SIgnal Classification) is an algorithm used for frequency estimation and radio direction finding. In many practical signal processing
MUSIC_(algorithm)
Measure of similarity between two graphs
of at least one algorithm is linear in the number of nodes while still being cubic in the node degree. Despite the above algorithms sometimes working
Graph_edit_distance
Graph which remains connected when fewer than k edges are removed
the max-flow min-cut theorem from the theory of network flows. Minimum vertex degree gives a trivial upper bound on edge-connectivity. That is, if a
Edge_connectivity
Mathematical construct in computer algebra
in his 1965 Ph.D. thesis, which also included an algorithm to compute them (Buchberger's algorithm). He named them after his advisor Wolfgang Gröbner
Gröbner_basis
Metaheuristic method for optimization problems
rules is summarized in § Algorithm 1, where we assume that an initial solution x is given. The output consists of a local minimum, denoted by x′, and its
Variable_neighborhood_search
Partition of a graph's nodes into cliques
pairs. Therefore, in triangle-free graphs, the minimum clique cover can be found by using an algorithm for maximum matching. The optimum partition into
Clique_cover
Problem in graph theory
opposite problem, that of finding a minimum cut is known to be efficiently solvable via the Ford–Fulkerson algorithm. As the maximum cut problem is NP-hard
Maximum_cut
One-by-one assignment of colors to graph vertices
coloring is a coloring of the vertices of a graph formed by a greedy algorithm that considers the vertices of the graph in sequence and assigns each
Greedy_coloring
Collective behavior of decentralized, self-organized systems
Monte Carlo algorithm for Minimum Feedback Arc Set where this has been achieved probabilistically via hybridization of Monte Carlo algorithm with Ant Colony
Swarm_intelligence
Type of load balancing
workload evenly across all nodes. Opportunistic Load Balancing (OLB) is the algorithm that assigns workloads to nodes in free order. It is simple but does not
Cloud_load_balancing
Computer compiler optimization technique
works followed up on the Poletto's linear scan algorithm. Traub et al., for instance, proposed an algorithm called second-chance binpacking aiming at generating
Register_allocation
American mathematician (1927–2017)
comparison sort with the fewest comparisons. For 20 years, this algorithm required the minimum number of comparisons. In 1963 along with his father Lester
L._R._Ford_Jr.
Parameter controlling the machine learning process
hyperparameters (such as the topology and size of a neural network) or algorithm hyperparameters (such as the learning rate and the batch size of an optimizer)
Hyperparameter (machine learning)
Hyperparameter_(machine_learning)
Method for discovering interesting relations between variables in databases
Then we will prune the item set by picking a minimum support threshold. For this pass of the algorithm we will pick 3. Since all support values are three
Association_rule_learning
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