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Least-weight tree connecting graph vertices
In graph theory, a minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph
Minimum_spanning_tree
the edges of which is lowest among all spanning trees of G {\displaystyle G} , is called a minimum spanning tree (MST). It is not necessarily unique. More
Parallel algorithms for minimum spanning trees
Parallel_algorithms_for_minimum_spanning_trees
Algorithm which can do multiple operations in a given time
Multiple-agent system (MAS) Parallel algorithms for matrix multiplication Parallel algorithms for minimum spanning trees Parallel computing Parareal Blelloch
Parallel_algorithm
Method for finding minimum spanning trees
In computer science, Prim's algorithm is a greedy algorithm that finds a minimum spanning tree for a weighted undirected graph. This means it finds a subset
Prim's_algorithm
Tree which includes all vertices of a graph
use algorithms that gradually build a spanning tree (or many such trees) as intermediate steps in the process of finding the minimum spanning tree. The
Spanning_tree
Method for finding minimum spanning trees
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
Borůvka's_algorithm
Minimum spanning forest algorithm that greedily adds edges
Kruskal's algorithm finds a minimum spanning forest of an undirected edge-weighted graph. If the graph is connected, it finds a minimum spanning tree. It is
Kruskal's_algorithm
Shortest network connecting points
and when a tree has degree six there is always another minimum spanning tree with maximum degree five. Three-dimensional minimum spanning trees have degree
Euclidean minimum spanning tree
Euclidean_minimum_spanning_tree
The distributed minimum spanning tree (MST) problem involves the construction of a minimum spanning tree by a distributed algorithm, in a network where
Distributed minimum spanning tree
Distributed_minimum_spanning_tree
Algorithm for the directed version of the minimum spanning tree problem
graph theory, Edmonds' algorithm or Chu–Liu/Edmonds' algorithm is an algorithm for finding a spanning arborescence of minimum weight (sometimes called
Edmonds'_algorithm
155–162, Bibcode:2017PaReL..87..155S, doi:10.1016/j.patrec.2016.06.001 Information on the PHMSF algorithm (Parallel Heuristic for Minimum Spanning Forests)
Minimum spanning tree-based segmentation
Minimum_spanning_tree-based_segmentation
Graph theory concept
minimum degree spanning tree of series-parallel graphs with small degrees. G. Yao, D. Zhu, H. Li, and S. Ma (2008) found a polynomial time algorithm that
Minimum_degree_spanning_tree
Abstract data type in computer science
shared-memory setting, the parallel priority queue can be easily implemented using parallel binary search trees and join-based tree algorithms. In particular, k_extract-min
Priority_queue
Algorithm for finding shortest paths
employed as a subroutine in algorithms such as Johnson's algorithm. The algorithm uses a min-priority queue data structure for selecting the shortest paths
Dijkstra's_algorithm
Sequence of locally optimal choices
overestimate path costs. Kruskal's algorithm and Prim's algorithm are greedy algorithms for constructing minimum spanning trees of a given connected graph. They
Greedy_algorithm
Subfield of mathematical optimization
optimization problems are the travelling salesman problem ("TSP"), the minimum spanning tree problem ("MST"), and the knapsack problem. In many such problems
Combinatorial_optimization
Overview of and topical guide to algorithms
to algorithms: An algorithm is a finite, well-defined sequence of instructions or rules for solving a problem or performing a computation. Algorithms are
Outline_of_algorithms
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
Area of discrete mathematics
random edge weights and using the minimum spanning tree for those weights. Random recursive tree, increasingly labelled trees, which can be generated using
Graph_theory
Optimization algorithm
ant colony algorithms for best-effort routing in datagram networks," Proceedings of the Tenth IASTED International Conference on Parallel and Distributed
Ant colony optimization algorithms
Ant_colony_optimization_algorithms
Taiwanese-American computer scientist
cited algorithms for scheduling tree-structured tasks,[H61a] the widest path problem,[H61b] optimal binary search trees,[HT71] linear layouts of trees and
T._C._Hu
Algorithm that combines multiple sorted lists into one
sorted order. These algorithms are used as subroutines in various sorting algorithms, most famously merge sort. The merge algorithm plays a critical role
Merge_algorithm
Optimization technique
constitute metaheuristic algorithms range from simple local search procedures to complex learning processes. Metaheuristic algorithms are approximate and usually
Metaheuristic
Generalization of depth-first search trees
theory, a Trémaux tree of an undirected graph G {\displaystyle G} is a type of spanning tree, generalizing depth-first search trees. They are defined
Trémaux_tree
Parallel computing algorithm
In parallel computing, work stealing is a scheduling strategy for multithreaded computer programs. It solves the problem of executing a dynamically multithreaded
Work_stealing
Class of algorithms that find approximate solutions to optimization problems
computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to optimization problems
Approximation_algorithm
Tree graph with all nodes within distance 1 from central path
the MSCP have linear time algorithms if a graph is an outerplanar, a series-parallel, or a Halin graph. Caterpillar trees have been used in chemical
Caterpillar_tree
Vector quantization algorithm minimizing the sum of squared deviations
efficient heuristic algorithms converge quickly to a local optimum. These are usually similar to the expectation–maximization algorithm for mixtures of Gaussian
K-means_clustering
Algorithm for linear programming
et al. is the representative of a branch of algorithms that apply fast matrix multiplication algorithms to linear programs. Linear–fractional programming
Simplex_algorithm
Data structure for storing non-overlapping sets
a key role in Kruskal's algorithm for finding the minimum spanning tree of a graph. The importance of minimum spanning trees means that disjoint-set data
Disjoint-set_data_structure
NP-hard problem in combinatorial optimization
above method gives the algorithm of Christofides and Serdyukov: Find a minimum spanning tree for the problem. Create a matching for the problem with the
Travelling_salesman_problem
Study of mathematical algorithms for optimization problems
of the simplex algorithm that are especially suited for network optimization Combinatorial algorithms Quantum optimization algorithms The iterative methods
Mathematical_optimization
Tree containing all suffixes of a given text
suffix trees, now known as Ukkonen's algorithm, with running time that matched the then fastest algorithms. These algorithms are all linear-time for a constant-size
Suffix_tree
Subset of a graph's nodes such that all other nodes link to at least one
efficient algorithm that can compute γ(G) for all graphs G. However, there are efficient approximation algorithms, as well as efficient exact algorithms for certain
Dominating_set
Graph with at most one cycle per component
augmented trees and maximal pseudoforests are also sometimes called augmented forests. The minimum spanning pseudoforest problem involves finding a spanning pseudoforest
Pseudoforest
topological minors Steiner tree, or Minimum spanning tree for a subset of the vertices of a graph. (The minimum spanning tree for an entire graph is solvable
List_of_NP-complete_problems
Binary tree derived from a sequence of numbers
pattern matching algorithms. A Cartesian tree for a sequence can be constructed in linear time. Cartesian trees are defined using binary trees, which are a
Cartesian_tree
Unsolved problem in parallel algorithms
lower bounds for several other problems in this computational model, including single-linkage clustering and geometric minimum spanning trees. However, proving
1-vs-2_cycles_problem
Chart displaying multivariate data
attribute, and the arrangement problem can be improve by using a minimum spanning tree. A prototype of this visualization is available as extension to
Parallel_coordinates
Algorithm for solving the quadratic programming problem from training SVMs
the chunking algorithm. In 1997, E. Osuna, R. Freund, and F. Girosi proved a theorem which suggests a whole new set of QP algorithms for SVMs. By the
Sequential minimal optimization
Sequential_minimal_optimization
Python module
path, etc. Support for several graph-theoretical algorithms: such as graph isomorphism, subgraph isomorphism, minimum spanning tree, connected components
Graph-tool
Optimization by removing non-optimal solutions to subproblems
records the minimum upper bound seen among all instances examined so far. The following is the skeleton of a generic branch-and-bound algorithm for minimizing
Branch_and_bound
Czech academic and mathematician
same algorithm has been rediscovered repeatedly. It is more suitable for distributed and parallel computation than many other minimum spanning tree algorithms
Otakar_Borůvka
Subfield of mathematical optimization
sets). Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard. A convex optimization
Convex_optimization
Algorithm used to solve non-linear least squares problems
other iterative optimization algorithms, the LMA finds only a local minimum, which is not necessarily the global minimum. The primary application of the
Levenberg–Marquardt_algorithm
Optimization algorithm
descent should not be confused with local search algorithms, although both are iterative methods for optimization. Gradient descent is particularly useful
Gradient_descent
Inverse function to a tower of powers
a set of points knowing the Euclidean minimum spanning tree: randomized O(n log* n) time. Fürer's algorithm for integer multiplication: O(n log n 2O(lg* n))
Iterated_logarithm
Property in graph theory
(2008). "Fixed-parameter algorithms for protein similarity search under mRNA structure constraints". Journal of Discrete Algorithms. 6 (4): 618–626. doi:10
Cutwidth
Mathematical algorithm
optimization algorithm that successively minimizes along coordinate directions to find the minimum of a function. At each iteration, the algorithm determines
Coordinate_descent
Measure of algorithm performance for large inputs
exploited in construction of algorithms, in addition to comparisons, then asymptotically faster algorithms may be possible. For example, if it is known that
Asymptotically optimal algorithm
Asymptotically_optimal_algorithm
Triangulation method
Santos, Francisco (2010). Triangulations, Structures for Algorithms and Applications. Algorithms and Computation in Mathematics. Vol. 25. Springer. Guibas
Delaunay_triangulation
Sequential model-based optimization of expensive black-box functions
or mixed-variable criteria. Examples include genetic algorithms and other evolutionary algorithms, as well as sequential Monte Carlo methods. Several derivative-free
Bayesian_optimization
Methodic assignment of colors to elements of a graph
coloring for a specific static or dynamic strategy of ordering the vertices, these algorithms are sometimes called sequential coloring algorithms. The maximum
Graph_coloring
Mathematical combinatorial optimization method
"Branch-Price-and-Cut Algorithms". Wiley Encyclopedia of Operations Research and Management Science. Savelsbergh, M. (1997). "A branch-and-price algorithm for the generalized
Branch_and_price
System with multiple networked computers
Humblet, and P. M. Spira (January 1983). "A Distributed Algorithm for Minimum-Weight Spanning Trees" (PDF). ACM Transactions on Programming Languages and
Distributed_computing
Optimization algorithm
1 February 2019. "NLopt Algorithms: SLSQP". Read the Docs. July 1988. Retrieved 1 February 2019. KNITRO User Guide: Algorithms Bonnans, J. Frédéric; Gilbert
Sequential quadratic programming
Sequential_quadratic_programming
Method to solve optimization problems
considered important enough to have much research on specialized algorithms. A number of algorithms for other types of optimization problems work by solving linear
Linear_programming
Mathematical optimization problem restricted to integers
Branch and bound algorithms have a number of advantages over algorithms that only use cutting planes. One advantage is that the algorithms can be terminated
Integer_programming
Finding multiple solutions of a problem
convergence to a single solution. The field of Evolutionary algorithms encompasses genetic algorithms (GAs), evolution strategy (ES), differential evolution
Evolutionary multimodal optimization
Evolutionary_multimodal_optimization
Optimization method
optimization, the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm is an iterative method for solving unconstrained nonlinear optimization problems. Like
Broyden–Fletcher–Goldfarb–Shanno algorithm
Broyden–Fletcher–Goldfarb–Shanno_algorithm
Graph representing faces of another graph
dual. For instance, cycles are dual to cuts, spanning trees are dual to the complements of spanning trees, and simple graphs (without parallel edges or
Dual_graph
Algorithm to compute the maximum flow in a flow network
to Algorithms (third ed.). MIT Press. pp. 727–730. ISBN 978-0-262-03384-8.{{cite book}}: CS1 maint: multiple names: authors list (link) Algorithms and
Edmonds–Karp_algorithm
Carlton E. Lemke. Lemke's algorithm is of pivoting or basis-exchange type. Similar algorithms can compute Nash equilibria for two-person matrix and bimatrix
Lemke's_algorithm
Collective behavior of decentralized, self-organized systems
general set of algorithms. Swarm prediction has been used in the context of forecasting problems. Similar approaches to those proposed for swarm robotics
Swarm_intelligence
Algorithms for solving convex optimization problems
IPMs) are algorithms for solving linear and non-linear convex optimization problems. IPMs combine two advantages of previously-known algorithms: Theoretically
Interior-point_method
American computer scientist
Johnson, D. B. (1975), "Priority queues with update and finding minimum spanning trees", Information Processing Letters, 4 (3): 53–57, doi:10.1016/0020-0190(75)90001-0
Donald_B._Johnson
Optimization algorithm
Pytlak, Radoslaw (2009). "Limited Memory Quasi-Newton Algorithms". Conjugate Gradient Algorithms in Nonconvex Optimization. Springer. pp. 159–190. ISBN 978-3-540-85633-7
Limited-memory_BFGS
Design technique for parallel algorithms
technique for parallel algorithms that operate on pointer structures, such as linked lists and directed graphs. Pointer jumping allows an algorithm to follow
Pointer_jumping
Numerical optimization algorithm
method, or polytope method) is a numerical method used to find a local minimum or maximum of an objective function in a multidimensional space. It is
Nelder–Mead_method
more of them will yield promising results, allowing for a more concentrated search nearby. The algorithm is implemented and described in terms of the explosion
Fireworks_algorithm
Optimization algorithm
node. Different choices for next nodes and starting nodes are used in related algorithms. Although more advanced algorithms such as simulated annealing
Hill_climbing
Metaheuristic proposed by Xin-She Yang
Swarm intelligence Yang, X. S. (2008). Nature-Inspired Metaheuristic Algorithms. Luniver Press. ISBN 978-1-905986-10-1. Almasi, Omid N.; Rouhani, Modjtaba
Firefly_algorithm
Concept in distributed computing
Humblet, and P. M. Spira (January 1983). "A Distributed Algorithm for Minimum-Weight Spanning Trees" (PDF). ACM Transactions on Programming Languages and
Leader_election
Canadian computer scientist (1944–2019)
recognition and machine learning, and showed that it contained the minimum spanning tree, and was a subgraph of the Delaunay triangulation. Three other well
Godfried_Toussaint
Technique for finding an extremum of a function
points, assuring that a minimum is contained between the outer points. The converse is true when searching for a maximum. The algorithm is the limit of Fibonacci
Golden-section_search
IEEE standard for Shortest Path Bridging
ECT-MASK[0] is reserved for a common spanning tree algorithm, while ECT-MASK[1] creates the Low PATHID set of shortest path first trees, ECT-MASK[2] creates
IEEE_802.1aq
Algorithm in mathematical optimization
regarded as the benchmark for maximum flow algorithms. Subcubic O(VElog(V 2/E)) time complexity can be achieved using dynamic trees, although in practice
Push–relabel maximum flow algorithm
Push–relabel_maximum_flow_algorithm
Sequential linear-quadratic programming (SLQP) is an iterative method for nonlinear optimization problems where objective function and constraints are
Sequential linear-quadratic programming
Sequential_linear-quadratic_programming
Primal-Dual algorithm optimization for convex problems
Xiaoqun; Chan, Tony F. (2010). "A General Framework for a Class of First Order Primal-Dual Algorithms for Convex Optimization in Imaging Science". SIAM Journal
Chambolle–Pock_algorithm
Computational task of sorting whole numbers
Michael L.; Willard, Dan E. (1994), "Trans-dichotomous algorithms for minimum spanning trees and shortest paths", Journal of Computer and System Sciences
Integer_sorting
Data structure that maintains info about the connected components of a graph
(2001). "Poly-logarithmic deterministic fully-dynamic algorithms for connectivity, minimum spanning tree, 2-edge, and biconnectivity". Journal of the ACM.
Dynamic_connectivity
Problem optimization method
Introduction to Algorithms (2nd ed.), MIT Press & McGraw–Hill, ISBN 0-262-03293-7 . pp. 344. Cormen, Thomas H. (2009). Introduction to Algorithms (3rd ed.)
Dynamic_programming
Subfield of convex optimization
problems. Other algorithms use low-rank information and reformulation of the SDP as a nonlinear programming problem (SDPLR, ManiSDP). Algorithms that solve
Semidefinite_programming
Algorithm for finding zeros of functions
MR 2265882. P. Deuflhard: Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms, Springer Berlin (Series in Computational
Newton's_method
Algorithmic optimization method
other test algorithms (often, comparison sorting algorithms). Advanced versions of the parametric search technique use a parallel algorithm as the test
Parametric_search
Smallest convex set containing a given set
pointwise minimum) and, in this form, is dual to the convex conjugate operation. In computational geometry, a number of algorithms are known for computing
Convex_hull
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
Graph width parameter
are the subcubic partial 2-trees. This means that their maximum degree is three and that they are subgraphs of series-parallel graphs. All other graphs
Carving_width
Solving multiple machine learning tasks at the same time
that system. Algorithms for multi-task optimization span a wide array of real-world applications. Recent studies highlight the potential for speed-ups in
Multi-task_learning
Algorithm for finding a local minimum of a function
Powell's conjugate direction method, is an algorithm proposed by Michael J. D. Powell for finding a local minimum of a function. The function need not be
Powell's_method
that of the Euclidean minimum spanning tree. Although known construction methods for them are slow, fast approximation algorithms with similar properties
Greedy_geometric_spanner
Form taken by the network of interconnections of a circuit
tree into the other (Kishi and Kajitani, p.323). Spanning forest. A forest of trees in which every node of the graph is visited by one of the trees.
Circuit_topology_(electrical)
Linear programming algorithm
holders of the patent on the RSA algorithm), who expressed the opinion that research proceeded on the basis that algorithms should be free. Even before the
Karmarkar's_algorithm
Optimization algorithm
performances of CS-base algorithms: Theoretical analysis on convergence of CS-based algorithms Providing the sufficient and necessary conditions for the control parameter
Cuckoo_search
Numerical approximation algorithm
criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of an iterative
Iterative_method
Israeli mathematician and computer scientist
several currently-fastest graph algorithms. Examples include trivalent graph isomorphism and minimum weight spanning trees. With his students, Galil devised
Zvi_Galil
Algorithm for solving linear programs
Column generation or delayed column generation is an efficient algorithm for solving large linear programs. The overarching idea is that many linear programs
Column_generation
Algorithm for solving linear programming problems
In mathematical optimization, affine scaling is an algorithm for solving linear programming problems. Specifically, it is an interior point method, discovered
Affine_scaling
Biconjugate gradient stabilized method Elijah Polak (1997). Optimization : Algorithms and Consistent Approximations. Springer-Verlag. ISBN 0-387-94971-2. v
Gradient_method
Form of Newton's method used in statistics
Jennrich, R. I. & Sampson, P. F. (1976). "Newton-Raphson and Related Algorithms for Maximum Likelihood Variance Component Estimation". Technometrics. 18
Scoring_algorithm
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