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Type of algorithm
A parameterized approximation algorithm is a type of algorithm that aims to find approximate solutions to NP-hard optimization problems in polynomial time
Parameterized approximation algorithm
Parameterized_approximation_algorithm
Class of algorithms that find approximate solutions to optimization problems
In computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to optimization problems
Approximation_algorithm
Type of approximation algorithm
computer science (particularly algorithmics), a polynomial-time approximation scheme (PTAS) is a type of approximation algorithm for optimization problems
Polynomial-time approximation scheme
Polynomial-time_approximation_scheme
Technique in numerical linear algebra
endfor The alternating projections algorithm exploits the fact that the low rank approximation problem, parameterized in the image form, is bilinear in
Low-rank_approximation
Problem in graph theory
approximation algorithm achieves an approximation ratio strictly less than one. There is a simple randomized 0.5-approximation algorithm: for each vertex
Maximum_cut
Problem of finding the longest simple path for a given graph
fixed-parameter tractable. The longest path problem, parameterized by clique-width, is hard for the parameterized complexity class W [ 1 ] {\displaystyle W[1]}
Longest_path_problem
Branch of computational complexity theory
Saket (2015). Parameterized Algorithms. Springer. ISBN 978-3-319-21274-6. Wiki on parameterized complexity Compendium of Parameterized Problems https://complexityzoo
Parameterized_complexity
Combinatorial optimization problem
issue by trying all values of k. A simple greedy approximation algorithm that achieves an approximation factor of 2 builds C {\displaystyle {\mathcal {C}}}
Metric_k-center
Subfield of mathematical optimization
polynomial time and find a solution that is close to optimal parameterized approximation algorithms that run in FPT time and find a solution close to the optimum
Combinatorial_optimization
Class of reinforcement learning algorithms
_{\theta }} is parameterized by a differentiable parameter θ {\displaystyle \theta } . In policy-based RL, the actor is a parameterized policy function
Policy_gradient_method
Subset of a graph's vertices, including at least one endpoint of every edge
several simple 2-factor approximations. It is a typical example of an NP-hard optimization problem that has an approximation algorithm. Its decision version
Vertex_cover
Estimate of time taken for running an algorithm
know quasi-polynomial time algorithms, but no polynomial time algorithm is known. Such problems arise in approximation algorithms; a famous example is the
Time_complexity
On short connecting nets with added points
APX-complete and thus does not admit a PTAS, unless P = NP. However, a parameterized approximation scheme exists, which for any ε > 0 {\displaystyle \varepsilon
Steiner_tree_problem
Reinforcement learning algorithms
The actor-critic algorithm (AC) is a family of reinforcement learning (RL) algorithms that combine policy-based RL algorithms such as policy gradient methods
Actor-critic_algorithm
A fully polynomial-time approximation scheme (FPTAS) is an algorithm for finding approximate solutions to function problems, especially optimization problems
Fully polynomial-time approximation scheme
Fully_polynomial-time_approximation_scheme
Task of computing complete subgraphs
best known lower bound is Ω(n), but no matching algorithm is known for the case of k ≥ 3. Parameterized complexity is the complexity-theoretic study of
Clique_problem
Probabilistic problem-solving algorithm
experiments or Monte Carlo simulations, are a broad class of computational algorithms based on repeated random sampling for obtaining numerical results, conceptualized
Monte_Carlo_method
{\displaystyle \Gamma } . An instance of a parameterized problem consists of (x,k), where k is called the parameter. A parameterized problem Π {\displaystyle \Pi }
Bidimensionality
Annual conference series on algorithms
International Symposium on Parameterized and Exact Computation, founded in 2004 and formerly the International Workshop on Parameterized and Exact Computation
European Symposium on Algorithms
European_Symposium_on_Algorithms
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
Dominating_set
Unsolved problem in computer science
polynomial function on the size of the input to the algorithm. The general class of questions that some algorithm can answer in polynomial time is "P" or "class
P_versus_NP_problem
Measure of similarity between two graphs
often implemented as an A* search algorithm. In addition to exact algorithms, a number of efficient approximation algorithms are also known. Most of them have
Graph_edit_distance
Probability distribution
variables, each of which has a mean of θ. The gamma distribution can be parameterized in terms of a shape parameter α and an inverse scale parameter β = 1/θ
Gamma_distribution
Combinatorial optimization graph problem
time approximation schemes (PTAS) were discovered for those problems. While the minimum k-cut problem is W[1]-hard parameterized by k, a parameterized approximation
Minimum_k-cut
Mathematical optimization problem restricted to integers
Koutecký, Martin; Levin, Asaf; Onn, Shmuel (2018). "A parameterized strongly polynomial algorithm for block structured integer programs". In Chatzigiannakis
Integer_programming
Number of vertices with unambiguous distances
S2CID 231979414 Lokshtanov, Daniel (2010), "Open problems – Parameterized complexity and approximation algorithms: Metric Dimension", in Demaine, Erik D.; Hajiaghayi
Metric dimension (graph theory)
Metric_dimension_(graph_theory)
Vertices whose removal breaks all cycles
existence of an approximation preserving L-reduction from the vertex cover problem to it; Existing constant-factor approximation algorithms. The best known
Feedback_vertex_set
Point set triangulation minimizing total length
polynomial-time approximation algorithms, see Plaisted & Hong (1987) (log-factor approximation) and Levcopoulos & Krznaric (1998) (constant-factor approximation). Cheng
Minimum-weight_triangulation
Curve used in computer graphics and related fields
approximation algorithms have been proposed and used in practice. The rational Bézier curve adds adjustable weights to provide closer approximations to
Bézier_curve
2D geometric minimization problem
polynomial-time approximation algorithm with a ratio smaller than 3 / 2 {\displaystyle 3/2} unless P = N P {\displaystyle P=NP} . However, the best approximation ratio
Strip_packing_problem
Lossless compression algorithm
are possible, and a dynamic programming algorithm is used to select an optimal one under certain approximations. Prior to LZMA, most encoder models were
LZMA
number associated with the graph, used to study the parameterized complexity of graph algorithms. Intuitively, it measures how similar the graph is to
Twin-width
Technique to solve partial differential equations
{\displaystyle {\mathcal {N}}[\cdot ;\lambda ]} is a nonlinear operator parameterized by λ {\displaystyle \lambda } , and Ω {\displaystyle \Omega } is a subset
Physics-informed neural networks
Physics-informed_neural_networks
Algorithm for virtual memory implementation
recently used) approximations and working set algorithms. Since then, some basic assumptions made by the traditional page replacement algorithms were invalidated
Page_replacement_algorithm
Method in computational phylogenetics
S2CID 14297537. Chen, Jianer; Fan, Jia-Hao; Sze, Sing-Hoi (2015). "Parameterized and approximation algorithms for maximum agreement forest in multifurcating trees"
Tree_rearrangement
P=NP. On the other hand, it was shown that a parameterized 3 / 2 {\displaystyle 3/2} -approximation algorithm with a runtime of 2 O ( k h log h ) n O (
Highway_dimension
Probability distribution
algorithm by West (2009) combines Hart's algorithm 5666 with a continued fraction approximation in the tail to provide a fast computation algorithm with
Normal_distribution
Method in numerical analysis
continuation is a method of computing approximate solutions of a system of parameterized nonlinear equations, F ( u , λ ) = 0. {\displaystyle F(\mathbf {u}
Numerical_continuation
Discrete probability distribution
\beta )} denote that λ is distributed according to the gamma density g parameterized in terms of a shape parameter α and an inverse scale parameter β: g
Poisson_distribution
Data structure for approximate set membership
hashing techniques were applied. He gave the example of a hyphenation algorithm for a dictionary of 500,000 words, out of which 90% follow simple hyphenation
Bloom_filter
Edges that hit all cycles in a graph
polynomial-time approximation scheme, which generalizes to a weighted version of the problem. A subexponential parameterized algorithm for weighted feedback
Feedback_arc_set
Straight path on a curved surface or a Riemannian manifold
of different ways to parameterize the shortest path. It is simpler to restrict the set of curves to those that are parameterized "with constant speed"
Geodesic
French computer scientist
problems from the points of view of parameterized complexity, fine-grained complexity, approximation algorithms, and regret. Bazgan earned her Ph.D.
Cristina_Bazgan
Calculation of complex statistical distributions
past Integrated nested Laplace approximations Markov chain central limit theorem Metropolis-adjusted Langevin algorithm Robert, Christian; Casella, George
Markov_chain_Monte_Carlo
Complexity class
NP-complete problems are often addressed by using heuristic methods and approximation algorithms. A decision problem C {\displaystyle \scriptstyle C} is NP-complete
NP-completeness
Computer-aided geometric design
progressive-iterative approximation (PIA) can be divided into interpolation and approximation schemes. In interpolation algorithms, the number of control
Progressive-iterative approximation method
Progressive-iterative_approximation_method
Branch of machine learning
is the number of hidden layers plus one (as the output layer is also parameterized). For recurrent neural networks, in which a signal may propagate through
Deep_learning
Turkish mathematician
are as follows: Onus, M. ve Richa, A.W.(2016). "Parameterized maximum and average degree approximation in topic based publish subscribe overlay network
Melih_Onuş
Matrix decomposition
applications of the SVD include computing the pseudoinverse, matrix approximation, and determining the rank, range, and null space of a matrix. The SVD
Singular_value_decomposition
Category of routing problem minimizing total distance and time
Cristina R. Delgado Serna & Joaquín Pacheco Bonrostro applied approximation algorithms to find the best school bus routes in the Spanish province of Burgos
Arc_routing
Any planar graph can be subdivided by removing a few vertices
location, algorithms for polygon triangulation, shortest paths, and the construction of nearest neighbor graphs, and approximation algorithms for the maximum
Planar_separator_theorem
Representation of a graph as a path graph "thickened" by some amount
best known approximation ratio of a polynomial time approximation algorithm for pathwidth is O((log n)3/2). For earlier approximation algorithms for pathwidth
Pathwidth
Logic problem, AND of pairwise ORs
assignment that maximizes the number of satisfied constraints, has an approximation algorithm whose optimality depends on the unique games conjecture, and another
2-satisfiability
Discrete Algorithms, Philadelphia, Pennsylvania: SIAM, pp. 1557–1576, MR 3202998 Moser, Hannes; Sikdar, Somnath (2009), "The parameterized complexity
Induced_matching
Measure of similarity between curves
discrete Fréchet distance, also called the coupling distance, is an approximation of the Fréchet metric for polygonal curves, defined by Eiter and Mannila
Fréchet_distance
Machine Approximation algorithm Simulated annealing Ant colony optimization algorithms Game semantics Generalized game Multiple-agent system Parameterized complexity
List of computability and complexity topics
List_of_computability_and_complexity_topics
Number denoting a graph's closeness to a tree
is commonly used as a parameter in the parameterized complexity analysis of graph algorithms. Many algorithms that are NP-hard for general graphs, become
Treewidth
is NP-complete. An approximation algorithm with approximation ratio 2 was provided by Frederickson & Ja'Ja' (1981). A parameterized and weighted version
Strong connectivity augmentation
Strong_connectivity_augmentation
Dominating set that induces a connected subgraph
(1998), "2-approximation algorithm for finding a spanning tree with maximum number of leaves", Proc. 6th European Symposium on Algorithms (ESA'98), Lecture
Connected_dominating_set
the parameterized complexity of biclique cover and partition", in Guo, Jiong; Hermelin, Danny (eds.), 11th International Symposium on Parameterized and
Graham–Pollak_theorem
Type of computational problem
problem admits an r-approximation algorithm, then the conflict-free geometric cover problem admits a similar approximation algorithm in FPT time. Vazirani
Covering_problems
Evolutionary algorithm
quadratic approximation. The update equations for mean and covariance matrix maximize a likelihood while resembling an expectation–maximization algorithm. The
CMA-ES
assignment to the variables in the clauses. We say that an algorithm A provides an α-approximation to MAXEkSAT if, for some fixed positive α less than or
MAXEkSAT
Maximum number of colors obtainable by a greedy graph coloring algorithm
approximate the Grundy number to within an approximation ratio better than c. There is an exact exponential time algorithm for the Grundy number that runs in
Grundy_number
Problem in computer science
can only be achieved if P = NP. An approximation within a factor of 2 can be achieved with this simple algorithm, however: Output the solution in which
MAX-3SAT
Multiple-winner electoral system
Kaczmarczyk, Andrzej; Knop, Dusan; Niedermeier, Rolf (2020). "Parameterized Algorithms for Finding a Collective Set of Items". Proceedings of the AAAI
Proportional_approval_voting
Technique for dimensionality reduction
objects are modeled by distant points with high probability. The t-SNE algorithm comprises two main stages. First, t-SNE constructs a probability distribution
T-distributed stochastic neighbor embedding
T-distributed_stochastic_neighbor_embedding
Technique in mathematical modeling
the application of reduced basis methods to parameterized partial differential equations. All algorithms in pyMOR are formulated in terms of abstract
Model_order_reduction
Numerical optimization algorithm
towards higher expected fitness. The general procedure is as follows: the parameterized search distribution is used to produce a batch of search points, and
Natural_evolution_strategy
Branch of chemistry
advances in DFT aim to reduce this complexity through various approximations and algorithmic improvements. There have also been significant speed improvements
Computational_chemistry
On linear-time algorithms for graph logic
As a result they obtain a fixed-parameter tractable algorithm for these problems, parameterized by a single parameter, treewidth, improving previous
Courcelle's_theorem
Graph drawing with vertices in horizontal layers
(1990), "Approximation algorithms for the maximum acyclic subgraph problem", Proceedings of the 1st ACM-SIAM Symposium on Discrete Algorithms (SODA'90)
Layered_graph_drawing
Artificial neural network node function
be a universal function approximator. This is known as the Universal Approximation Theorem. The identity activation function does not satisfy this property
Activation_function
Set of hypergraph nodes to which every hyperedge is connected
d-hitting set permits a d-approximation algorithm. Assuming the unique games conjecture, this is the best constant-factor algorithm that is possible and otherwise
Vertex_cover_in_hypergraphs
Function of four real variables that defines how light is reflected at an opaque surface
\omega _{\text{i}}} . Each direction ω {\displaystyle \omega } is itself parameterized by azimuth angle ϕ {\displaystyle \phi } and zenith angle θ {\displaystyle
Bidirectional reflectance distribution function
Bidirectional_reflectance_distribution_function
Machine learning framework
has a respective local operator W t {\displaystyle W_{t}} (usually parameterized by a pointwise neural network), a kernel integral operator K t {\displaystyle
Neural_operators
Non-linear statistical modeling software suite
function minimizer; an algorithm to check that the derivatives are correct with respect to finite difference approximations; an algorithm to insert model parameters
ADMB
In Bayesian probability theory
to statistical problems such as the Laplace approximation, Gibbs/Metropolis sampling, or the EM algorithm. It is also possible to apply the above considerations
Marginal_likelihood
Rewriting system and type of formal grammar
significant effort involved, the resulting system provided only an approximation of the tree's growth, illustrating the challenges of manually encoding
L-system
Lower bound on the log-likelihood of some observed data
special case when the approximate posterior and the prior are both parameterized as Gaussians, since then the KL term (though it is itself an expectation)
Evidence_lower_bound
Unit hypercube of variable dimension whose corners have been perturbed
basis-exchange pivoting algorithms and also for interior-point algorithms. The Klee–Minty cube was originally specified with a parameterized system of linear
Klee–Minty_cube
Probability distribution and special case of gamma distribution
or the chi-squared approximation for a small sample size. Similarly, in analyses of contingency tables, the chi-squared approximation will be poor for a
Chi-squared_distribution
Polynomial equation whose integer solutions are sought
However, Hilbert's tenth problem shows that there cannot exist a general algorithm that can decide whether an arbitrary Diophantine equation has an integer
Diophantine_equation
Algorithm that estimates unknowns from a series of measurements over time
As such, it is a common sensor fusion and data fusion algorithm. Noisy sensor data, approximations in the equations that describe the system evolution,
Kalman_filter
General-purpose functional programming language
structures and algorithms. One popular algorithm for breadth-first search of trees makes use of queues. Here is a version of that algorithm parameterized over an
Standard_ML
Notion in combinatorics
events. In this context, there are two important notions of approximation, both parameterized by a number ε {\displaystyle \varepsilon } : a set S {\displaystyle
Sauer–Shelah_lemma
Graph used in computational complexity theory and graph theory
programming based approximation algorithms for the vertex cover and graph coloring problems. Their properties with respect to these algorithms have been used
Frankl–Rödl_graph
Partitioning a digital image into segments
strategies work well in practice. Classical algorithms are graduated non-convexity and Ambrosio-Tortorelli approximation. Graph partitioning methods are an effective
Image_segmentation
an efficient algorithm for the egalitarian Monroe rule. Lu and Boutilier presented a polytime 0.63-factor approximation greedy algorithm for the optimal
Fully proportional representation
Fully_proportional_representation
Graph with at most one crossing per edge
Michael J.; Cabello, Sergio; Eppstein, David (2013), "Parameterized complexity of 1-planarity", Algorithms and Data Structures Symposium (WADS 2013), vol. 22
1-planar_graph
Israeli mathematician
Marx (2018). "Covering a tree with rooted subtrees - parameterized and approximation algorithms" (PDF). SODA: 2801–2820. Shmuel Onn; Uriel Rothblum (2004)
Shmuel_Onn
Numerical invariant of graphs
time algorithm based on the planarity of the excluded minors for tree-depth was given earlier by Bodlaender et al. (1998). For improved parameterized algorithms
Tree-depth
Research topic in computational geometry
ICP Algorithm" (PDF). "Chris Tralie : Laplacian Meshes". www.ctralie.com. Retrieved 2017-03-16. Desbrun, Mathieu (2002). "Intrinsic Parameterizations of
Geometry_processing
Machine learning and applied statistics
a multivariate function). In a probabilistic numerical algorithm, this process of approximation is thought of as a problem of estimation, inference or
Probabilistic_numerics
Property in graph theory
, the running time of this algorithm is 2 O ( c 2 ) n {\textstyle 2^{O(c^{2})}n} . An alternative parameterized algorithm, more suitable for graphs in
Cutwidth
Statistical method of dividing data into equal-sized intervals for analysis
nonparametric estimation algorithms in particular. There are a number of such algorithms such as those based on stochastic approximation or Hermite series estimators
Quantile
Generalization of the concept of parallel lines
{\vec {x}}(t)=(x(t),y(t))} , and you have a second curve that can be parameterized by its unit normal, d → ( n → ) {\displaystyle {\vec {d}}({\vec {n}})}
Parallel_curve
Subgraph
Henning; Prieto, Elena; Rosamond, Frances (2006), "Nonblocker: Parameterized algorithmics for minimum dominating set" (PDF), SOFSEM 2006: 32nd Conference
Nonblocker
Deep learning generative model to encode data representation
q-distributions, or variational posteriors. These q-distributions are normally parameterized for each individual data point in a separate optimization process. However
Variational_autoencoder
Conceptual framework used in numerical analysis of surfaces and shapes
this transformation numerically by parameterizing the boundary of the shape and following its evolution. An algorithm can be used to detect the moment the
Level-set_method
PARAMETERIZED APPROXIMATION-ALGORITHM
PARAMETERIZED APPROXIMATION-ALGORITHM
PARAMETERIZED APPROXIMATION-ALGORITHM
PARAMETERIZED APPROXIMATION-ALGORITHM
Girl/Female
English
Abbreviation of Tatiana.
Girl/Female
American, British, English, French, German
Cheerful; Derived from Lacey which is a French Nobleman's Surname Brought to British Isles After Norman Conquest
Girl/Female
Bengali, Christian, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Telugu
Manuscripts of God
Surname or Lastname
English
English : variant of Bubb.German : variant of Bopp.
Boy/Male
Hindu
Method, Way, Mode, Manner, One who crosses the river of life, Morning star
Boy/Male
American, Arabic, Australian, Turkish
Handsome; Camel
Boy/Male
Celtic Irish
Blond.
Girl/Female
Hindu, Indian
Beautiful
Girl/Female
Indian
Goddess of will, Companion
Girl/Female
Hindu, Indian
Splendour; Beauty; Ornament
PARAMETERIZED APPROXIMATION-ALGORITHM
PARAMETERIZED APPROXIMATION-ALGORITHM
PARAMETERIZED APPROXIMATION-ALGORITHM
PARAMETERIZED APPROXIMATION-ALGORITHM
PARAMETERIZED APPROXIMATION-ALGORITHM
a.
Pertaining to the first in time of the three subdivisions into which the Tertiary formation is divided by geologists, and alluding to the approximation in its life to that of the present era; as, Eocene deposits.
n.
The act of approximating; a drawing, advancing or being near; approach; also, the result of approximating.
a.
Resembling, or approximating to, a hemisphere in form.
adv.
With approximation; so as to approximate; nearly.
n.
Alt. of Algorithm
n.
The art of calculating by nine figures and zero.
n.
One who, or that which, approximates.
n.
The act of violently forcing air out through the nasal passages while the cavity of the mouth is shut off from the pharynx by the approximation of the soft palate and the base of the tongue.
n.
A value that is nearly but not exactly correct.
p. pr. & vb. n.
of Approximate
n. pl.
A group of ganoid fishes, including the living genera Ceratodus and Lepidosiren, which present the closest approximation to the Amphibia. The air bladder acts as a lung, and the nostrils open inside the mouth. See Ceratodus, and Illustration in Appendix.
a.
Approaching; approximate.
n.
The art of calculating with any species of notation; as, the algorithms of fractions, proportions, surds, etc.
v. t.
To mention or suggest as an estimate, hypothesis, or approximation; hence, to suppose; -- in the imperative, followed sometimes by the subjunctive; as, he had, say fifty thousand dollars; the fox had run, say ten miles.
n.
The transient approximation of the edges of a natural opening; imperforation.
n.
An approach to a correct estimate, calculation, or conception, or to a given quantity, quality, etc.
n.
A continual approach or coming nearer to a result; as, to solve an equation by approximation.