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Mathematical concept in graph theory
In graph theory, an efficient dominating set (also called an e.d. set or independent perfect dominating set) is a dominating set with the additional property
Efficient_dominating_set
Subset of a graph's nodes such that all other nodes link to at least one
graph classes. Dominating sets are of practical interest in several areas. In wireless networking, dominating sets are used to find efficient routes within
Dominating_set
Argentine-born American mathematician
worst-case efficient dominating sets in digraphs are conceived so that their presence in certain strong digraphs corresponds to that of efficient dominating sets
Italo_Jose_Dejter
them important examples in the study of domination in graphs. An efficient dominating set is also known as a 1-perfect code. S ( n , 1 ) {\displaystyle S(n
Sierpiński_graph
Dominating set that induces a connected subgraph
all connected dominating sets of G. The connected domination number of G is the number of vertices in the minimum connected dominating set. Any spanning
Connected_dominating_set
Set preferred to any other by a majority
the set is known as a dominating set. Thus the Smith set is also called the smallest dominating set. The Schwartz set is equivalent to the Smith set, except
Smith_set
Set of all Pareto efficient situations
Pareto front (also called Pareto frontier or Pareto curve) is the set of all Pareto efficient solutions. Colloquially, this means when there are many distinct
Pareto_front
Weakly optimal allocation of resources
context of efficiency in production vs. x-inefficiency: a set of outputs of goods is Pareto efficient if there is no feasible re-allocation of productive inputs
Pareto_efficiency
Mathematical concept
efficient set can be specified by choosing the portfolio shares to maximize the function μ P − b σ P {\displaystyle \mu _{P}-b\sigma _{P}} ; the set of
Multi-objective_optimization
Classical problem in combinatorics
{\displaystyle k} sets to cover as many elements as possible. Dominating set is the problem of selecting a set of vertices (the dominating set) in a graph such
Set_cover_problem
Generalization of dominating sets using fractional weights
{\displaystyle v} . Not all graphs admit efficient fractional dominating functions. A fractional total dominating function requires that for every vertex
Fractional_dominating_set
When every path in a control-flow graph must go through one node to reach another
is an efficient method of computing control dependence, which is critical to the analysis. Memory usage analysis can benefit from the dominator tree to
Dominator_(graph_theory)
2016 film by Tim Miller
got us to a place where Fox was willing to make it. The script was very efficient and not too long. That was a function of budget more than anything, but
Deadpool_(film)
Independent set which is not a subset of any other independent set
set {a, c}. In this same graph, the maximal cliques are the sets {a, b} and {b, c}. A MIS is also a dominating set in the graph, and every dominating
Maximal_independent_set
Quality of a strategy in game theory
Therefore, we can say "B dominates A" to mean "B weakly dominates A".) B is weakly dominated by A: there is at least one set of opponents' actions for
Strategic_dominance
Indian computer scientist (born 1965)
Guha designed an approximation algorithms for the minimum connected dominating set problem that achieves a factor of 2 ln Δ + O(1), where Δ is the maximum
Samir_Khuller
Unrelated vertices in graphs
another independent set is called maximal. Such sets are dominating sets. Every graph contains at most 3n/3 maximal independent sets, but many graphs have
Independent set (graph theory)
Independent_set_(graph_theory)
G {\displaystyle G} such that the dominating number γ ( G ) {\displaystyle \gamma (G)} equals the eternal dominating number γ {\displaystyle \gamma } ∞
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Complexity class of approximable problems
problems that can be approximated efficiently to within a factor logarithmic in the input size, includes min dominating set when degree is unbounded. Poly-APX-complete
APX
Algorithm that arranges lists in order
lexicographical order, and either ascending order or descending order. Efficient sorting is important for optimizing the efficiency of other algorithms
Sorting_algorithm
Processor executing one instruction in minimal clock cycles
expressed as follows: A RISC processor has an instruction set that is designed for efficient execution by a pipelined processor and for code generation
Reduced instruction set computer
Reduced_instruction_set_computer
item (EQ1). The problem of efficient approximately fair item allocation is to find an allocation that is both Pareto-efficient (PE) and satisfies one of
Efficient approximately fair item allocation
Efficient_approximately_fair_item_allocation
Type of fair division
Given a set of resources and a set of agents, the goal is to divide the resources among the agents in a way that is both Pareto efficient (PE) and envy-free
Efficient_envy-free_division
Method for speeding related binary searches
answered efficiently in terms of the intersection size h. One structure that can be used for this purpose is the convex layers of the input point set, a family
Fractional_cascading
Graph without four-vertex star subgraphs
reaches a dominating set no larger than D {\displaystyle D} , so in particular when the starting set D {\displaystyle D} is a minimum dominating set this process
Claw-free_graph
point set to one of maintaining the maximal points of a dynamic two-dimensional point set. The two-dimensional subproblem can be solved efficiently by using
Maxima_of_a_point_set
How many of a graph's edges must be removed to increase domination number
considers total dominating sets (where every vertex in the dominating set must also be adjacent to another vertex in the dominating set). The Roman bondage
Bondage_number
Set of edges without common vertices
matching with k edges is an edge dominating set with k edges. Conversely, if we are given a minimum edge dominating set with k edges, we can construct a
Matching_(graph_theory)
Similar division problem in economics and computer science
Efficient cake-cutting is a problem in economics and computer science. It involves a heterogeneous resource, such as a cake with different toppings or
Efficient_cake-cutting
Signal processing algorithm
They further described an efficient method for computing the times and frequencies for the reassigned spectrogram efficiently and accurately without explicitly
Reassignment_method
1999 film by Ulu Grosbard
is brilliant as an anxious mother consumed with finding her lost son. Dominating scene after scene, she conveys anguish and guilt in an all-out performance
The Deep End of the Ocean (film)
The_Deep_End_of_the_Ocean_(film)
Property of an intermediate representation in a compiler
the set of block-local variables is a simpler and faster procedure than full live-variable analysis, making semi-pruned SSA form more efficient to compute
Static_single-assignment_form
to x {\displaystyle x} . Via dominating pairs and the spine property. Every connected AT-free graph contains a dominating pair, a pair of vertices ( u
Asteroidal_triple-free_graph
Republican Primary". co/efficient. March 27, 2026. Retrieved March 27, 2026. "South Carolina 2026 Republican Primary". co/efficient. March 17, 2026. Retrieved
2026 South Carolina gubernatorial election
2026_South_Carolina_gubernatorial_election
Electronic circuit with two stable states
using two single-edge triggered D-type flip-flops and three XOR gates. An efficient functional alternative to a D flip-flop can be made with dynamic circuits
Flip-flop_(electronics)
Electric light that produces light using LEDs
lamps are significantly more energy-efficient than equivalent incandescent lamps and fluorescent lamps. The most efficient commercially available LED lamps
LED_lamp
Complete, full information, perfectly competitive markets are Pareto efficient
allocatively and productively efficient, which can be shown to follow from perfectly competitive factor and production markets. Given a set G {\displaystyle G}
Fundamental theorems of welfare economics
Fundamental_theorems_of_welfare_economics
Polis: DOGE is 'tearing down the old without necessarily having a more efficient way of doing it'". Politico. Retrieved February 20, 2025. When asked whether
2028 United States presidential election
2028_United_States_presidential_election
Chinese computer scientist
multiprocessors, local construction of connected dominating set and its applications in mobile ad hoc networks, and efficient routing in delay tolerant networks, including
Jie_Wu
graphs can be translated to words representing them and solved on words (efficiently)? The list of publications to study representation of graphs by words
Word-representable_graph
2016 film by Fede Álvarez
August 24, 2016. Retrieved August 27, 2016. "Don't Breathe is a ruthlessly efficient, claustrophobic terror machine". theverge.com. August 25, 2016. Retrieved
Don't_Breathe
Sequence of operations for a task
and the decorator pattern. An important aspect of algorithm design is efficient use of resources such as memory or time; the big O notation is used to
Algorithm
is called Pareto-efficient (PO) if it is not Pareto-dominated by any discrete allocation; it is called fractionally Pareto-efficient (fPO) if it is not
Fractional_Pareto_efficiency
How one process influences another
philosophers referred to as the 'New Mechanists' dominate the literature. For the scientific investigation of efficient causality, the cause and effect are each
Causality
Class of theorems about Nash equilibrium payoff profiles in repeated games
then it is Pareto efficient and weakly-coalition-individually-rational. On the other hand, if it is Pareto efficient and strongly-coalition-individually-rational
Folk_theorem_(game_theory)
Fictional universe created by Isaac Asimov
knowledge" that will enable society to revive itself more quickly and efficiently. The Seldon Plan is Seldon's great work intended to achieve this goal
Foundation_universe
Operations research that evaluates multiple conflicting criteria in decision making
small set of good alternatives, or grouping alternatives into different preference sets. An extreme interpretation could be to find all "efficient" or "nondominated"
Multiple-criteria decision analysis
Multiple-criteria_decision_analysis
Standard example in game theory
from a self-interested standpoint, this Nash equilibrium is not Pareto efficient. The structure of the traditional prisoner's dilemma can be generalized
Prisoner's_dilemma
British television soap opera
studio are low emission vehicles and the production team take more efficient energy efficient generators out on location. Caterers no longer use polystyrene
EastEnders
Large language model by Meta AI
training data, rather than the number of parameters, reasoning that the dominating cost for LLMs is from doing inference on the trained model rather than
Llama_(language_model)
Solution concept of a non-cooperative game
communication. In fact, strong Nash equilibrium has to be weakly Pareto efficient. As a result of these requirements, strong Nash is too rare to be useful
Nash_equilibrium
Professional basketball tournament
the way with 30 points and 11 assists, Anthony Davis finished with an efficient 17 points and 15 rebounds, shooting 72.7% from the field, while Austin
2024_NBA_playoffs
Brazilian kickboxer and mixed martial artist (born 1987)
kicks to slow his opponents down and set up power shots. While his pace isn’t particularly high, he’s extremely efficient—many of his strikes are thrown with
Alex_Pereira
Fuel economy standards in the U.S.
EPA and NHTSA was named the Safer Affordable Fuel-Efficient (SAFE) Vehicle Rules. It aimed to set new CAFE standards for MY 2022–2026 passenger car and
Corporate average fuel economy
Corporate_average_fuel_economy
Method for recursively subdividing a space into two subsets using hyperplanes
potentially visible sets to accelerate visible surface determination in orthogonal 2D environments. 1991 Gordon and Chen described an efficient method of performing
Binary_space_partitioning
Structuring text as input to generative artificial intelligence
what to draw. Heikkilä, Melissa (September 16, 2022). "This Artist Is Dominating AI-Generated Art and He's Not Happy About It". MIT Technology Review.
Prompt_engineering
Concept in sociology
calculating efficient system. But now such religious views are no longer needed to sustain capitalism. Moreover, the systematic efficient calculations
Iron_cage
Line of smartwatches
Calling, enabling emergency calls in over 150 countries, a more energy-efficient S5 processor, improved ambient light sensor, and storage doubled to 32 GB
Apple_Watch
was announced immediately after the conclusion of the second season. It is set to premiere in October 2027. Official English title, per Crunchyroll's home
List_of_Frieren_episodes
Season of television series
October 1, 2025. Pucci, Douglas (October 8, 2025). "Sunday Ratings: FS1 Dominates Cable in Prime Time with MLB Postseason". Programming Insider. Retrieved
Bob's_Burgers_season_16
Simulation of the sense of smell
backtrack then move in another random direction. This method is simple and efficient, however, the length of the path is highly variable and missteps increase
Machine_olfaction
Capital and most populous city of Sweden
management, urban planning, carbon dioxide emissions, and sustainable and efficient transportation system, among others. According to the European Cities
Stockholm
Type of algorithm
solution, the problem is W[2]-hard (due to a folklore reduction from the Dominating Set problem). Steiner Tree is also known to be APX-hard. However, there
Parameterized approximation algorithm
Parameterized_approximation_algorithm
Professional basketball tournament
cruised to a win against the Lakers in the opening game of the series, dominating from the second quarter onwards. Anthony Edwards recorded a near-triple-double
2025_NBA_playoffs
2024 animated film by Disney
internal conflicts. Owen Gleiberman (Variety) called it "an okay movie" and "efficient enough" to be a holiday hit, though far more product-like than its predecessor
Moana_2
Rajmohan Rajaraman, Torsten Suel, "An efficient distributed algorithm for constructing small dominating sets" Distributed Computing 15(3) pp. 193–205
Torsten_Suel
Game where groups of players may enforce cooperative behaviour
\varepsilon } that makes the set non-empty (Bilbao 2000). The Shapley value is the unique payoff vector that is efficient, symmetric, and satisfies monotonicity
Cooperative_game_theory
System that transfers heat from one space to another
outdoors. As it transfers rather than generates heat, it is more energy-efficient than heating by gas boiler. In a typical vapor-compression heat pump,
Heat_pump
2010 American horror film by Breck Eisner
3½ stars of 4, adding he "greatly prefer this cleverly sustained and efficiently relentless remake to the '73 edition. It is lean and simple." Eric M
The_Crazies_(2010_film)
Generalization of tree graphs to hypergraphs
Andreas; Leitert, Arne; Rautenbach, Dieter (2012), "Efficient dominating and edge dominating sets for graphs and hypergraphs", Algorithms and Computation:
Hypertree
American professional boxer (born 1994)
Retrieved December 20, 2025. "Alycia Baumgardner goes the distance in dominating Leila Beaudoin". Boxing Scene. Retrieved December 20, 2025. "Alycia Baumgardner
Alycia_Baumgardner
Energy-efficient landscaping is a type of landscaping designed for the purpose of conserving energy. There is a distinction between the embedded energy
Energy-efficient_landscaping
American entrepreneur and venture capitalist (born 1967)
still prioritize democratic decision-making, even at the risk of less efficient outcomes. In his book L'Empire de l'ombre, Da Empoli echoes the sentiment
Peter_Thiel
North America basketball championship
they missed 20 of their first 22 three-point attempts; however, Jokic's efficient 12 of 16 shooting from the field provided a much-needed boost, as he was
2023_NBA_Finals
Period of rapid progress in AI
becomes more sophisticated, it may eventually become cheaper and more efficient than human workers, which could cause technological unemployment and a
AI_boom
Recursive integer sequence
was the start of a dominating circular shift before anything was removed. For example, consider XXYXY. This sequence is dominating, but none of its circular
Catalan_number
2010 American crime thriller film directed by Ben Affleck
"That sequence, like most of the other action set pieces in the film, is lean, brutal, and efficient, and evidence of Mr. Affleck's skill and self-confidence
The_Town_(2010_film)
Japanese anime television series
connections with large corporations and national organizations. She is efficient and does her job without being swayed by emotions. She can be frightening
Lazarus_(Japanese_TV_series)
2022 film by Domee Shi
"Pixar Celebrates All-Female Leadership Team of 'Turning Red': "The Most Efficient Film We've Ever Made"". The Hollywood Reporter. Archived from the original
Turning_Red
Study of mathematical algorithms for optimization problems
to be "Pareto optimal" (equivalently, "Pareto efficient" or in the Pareto set) if it is not dominated by any other design: If it is worse than another
Mathematical_optimization
Hybrid electric car by Honda
Honda's first model with Integrated Motor Assist system and the most fuel efficient gasoline-powered car available in the U.S. without plug-in capability
Honda_Insight
History and future of the universe
(such as the electron, muons and certain neutrinos) and antileptons, dominating the mass of the universe. Initially leptons and antileptons are produced
Chronology_of_the_universe
British science fiction television series (1965–1966)
device allowed shots of moving vehicles to be filmed on a static set to make efficient use of the limited studio space. Airborne aircraft shots were mounted
Thunderbirds_(TV_series)
is not Pareto dominated by another network then it is a Pareto efficient network. In the figure "An Example of Efficient, Pareto Efficient, and Pairwise
Strategic_network_formation
different "stable sets" (sets of residents that can be matched to it in a stable matching) is linear in n, and they can be enumerated efficiently. Moreover,
Optimal_stable_matching
graphs. Edge dominating set, dominating set, r-dominating set, connected dominating set, r-scattered set, minimum maximal matching, independent set, maximum
Bidimensionality
over Kathy Hochul in NY election race". New York Post. "Rep. Elise Stefanik set to drop her bid for NYS governor". Politico. December 19, 2025. "Labor troubles
2026 New York gubernatorial election
2026_New_York_gubernatorial_election
First President of Botswana (1921–1980)
enmity and corruption. The small public service was transformed into an efficient and relatively corruption-free bureaucracy with workers hired based on
Seretse_Khama
2026 single by Lady Gaga and Doechii
stim. Jon Pareles of The New York Times described the track as "a very efficient committee product" by its seven songwriters, but said Gaga and Doechii
Runway_(song)
2018 film by Leigh Whannell
give up control of his body, allowing STEM to turn Grey into a lethally efficient fighting machine, killing Serk with little effort. Cortez later sees drone
Upgrade_(film)
Westernmost region of the African continent
largest container ships to focus on a smaller number of large ports, while efficiently serving a larger hinterland. This line connects 3 ft 6 in (1,067 mm)
West_Africa
Combinatorial optimization problem
Jurij; Robič, Borut (2005). "Solving the k-center Problem Efficiently with a Dominating Set Algorithm". Journal of Computing and Information Technology
Metric_k-center
Property in graph theory
algorithms that are efficient for sparse graphs with suitably small input parameter values. In particular, finding a dominating set of size k, on t-biclique-free
Biclique-free_graph
Physical phenomenon
of atoms is not essential for the quantum reflection but it allows the efficient trapping and cooling using optical frequencies. In addition, the excitation
Quantum_reflection
1985 science fiction novel by Bruce Sterling
Shapers for decades, fighting over whose technology is more powerful and efficient. They originate from the asteroid belt's colonies. Moondocks: A derisive
Schismatrix
Analog of Pareto efficiency for situations with incomplete information
information. Under Pareto efficiency, an allocation of a resource is Pareto efficient if there is no other allocation of that resource that makes no one worse
Bayesian_efficiency
Graph whose maximal clique hypergraph is a hypertree
Andreas; Leitert, Arne; Rautenbach, Dieter (2012), "Efficient dominating and edge dominating sets for graphs and hypergraphs", in Chao, Kun-Mao; Hsu,
Dually_chordal_graph
production, and reap the benefits of transparent structure in the shape of efficient taxation. When French seamstresses attained guild privileges in 1675,
Guilds_in_medieval_Europe
public utilities. It attempts to set prices at efficient (non-monopolistic, competitive) levels equal to the efficient costs of production, plus a government-permitted
Rate-of-return_regulation
Algorithm for computing convex hulls in a set of points
hull algorithms Graham, R.L. (1972). "An Efficient Algorithm for Determining the Convex Hull of a Finite Planar Set" (PDF). Information Processing Letters
Graham_scan
EFFICIENT DOMINATING-SET
EFFICIENT DOMINATING-SET
Boy/Male
Indian, Sanskrit
Skillful; Efficient
Boy/Male
Tamil
Rahulraj | ராஹà¯à®²à®°à®¾à®œ
Efficient, Capable
Rahulraj | ராஹà¯à®²à®°à®¾à®œ
Boy/Male
Hindu, Indian, Punjabi, Sikh
Capable; Skilful; Efficient
Boy/Male
Hindu
Efficient, Capable
Girl/Female
Hindu
Durga, Agile, Efficient, Swift
Boy/Male
Tamil
Cleverness, Honesty, Brilliance, Efficient
Boy/Male
Indian, Punjabi, Sikh
Intelligent; Efficient
Girl/Female
Assamese, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Agile; Efficient
Boy/Male
Tamil
An efficient horse rider
Girl/Female
Hindu, Indian, Marathi, Sanskrit
Effective; Efficient; Goddess Durga
Boy/Male
Hindu
An efficient horse rider
Girl/Female
Tamil
Cleverness, Honesty, Brilliance, Efficient
Boy/Male
Tamil
Vishwadakshinah | விஷà¯à®µà®¾à®¤à®•à¯à®·à¯€à®¨à®¾à®¹
Skilfull and efficient Lord
Vishwadakshinah | விஷà¯à®µà®¾à®¤à®•à¯à®·à¯€à®¨à®¾à®¹
Girl/Female
Tamil
Durga, Agile, Efficient, Swift
Boy/Male
Hindu
Cleverness, Honesty, Brilliance, Efficient
Girl/Female
Gujarati, Indian
Efficient
Girl/Female
Arabic
Efficient
Girl/Female
Indian
Cleverness, Honesty, Brilliance, Efficient
Boy/Male
Hindu
Skilfull and efficient Lord
Boy/Male
Hindu, Indian, Marathi
An Efficient Architect
EFFICIENT DOMINATING-SET
EFFICIENT DOMINATING-SET
Girl/Female
Christian, Indian
God; Jesus
Girl/Female
Muslim
Princess
Girl/Female
Arabic, Muslim
Passion
Boy/Male
Muslim
Worshipper. Adorer.
Girl/Female
Tamil
Avanthika | அவஂதிகா
City of ujjain, Princess of ujjain
Girl/Female
Hindu, Indian
Goddess Lakshmi
Girl/Female
Indian, Punjabi, Sikh
Destined to be Heroic
Girl/Female
Muslim
Plenty
Girl/Female
Muslim
Calmness, Quietness
Girl/Female
Indian
Swan like
EFFICIENT DOMINATING-SET
EFFICIENT DOMINATING-SET
EFFICIENT DOMINATING-SET
EFFICIENT DOMINATING-SET
EFFICIENT DOMINATING-SET
a.
Wanting, to make up completeness; wanting, as regards a requirement; not sufficient; inadequate; defective; imperfect; incomplete; lacking; as, deficient parts; deficient estate; deficient strength; deficient in judgment.
n.
The act of ominating; presaging.
n.
Causing effects; producing results; that makes the effect to be what it is; actively operative; not inactive, slack, or incapable; characterized by energetic and useful activity; as, an efficient officer, power.
a.
Equal to the end proposed; adequate to wants; enough; ample; competent; as, provision sufficient for the family; an army sufficient to defend the country.
n.
The act of dominating; exercise of power in ruling; dominion; supremacy; authority; often, arbitrary or insolent sway.
p. pr. & vb. n.
of Dominate
a.
Making or doing throughly; efficient; effectual.
a.
Not efficient; not producing the effect intended or desired; inefficacious; as, inefficient means or measures.
a.
Self-sufficient; self-satisfied; content.
n.
Alt. of Efficiency
n.
An efficient cause; a prime mover.
a.
Sufficient for one's self without external aid or cooperation.
v. i.
Efficient; vigorous; brilliant.
a.
Ruminant; ruminating.
n.
A supposed high order of angels; dominations. See Domination, 3.
n.
The quality of being efficient or producing an effect or effects; efficient power; effectual agency.
n.
A number, commonly used in computation as a factor, expressing the amount of some change or effect under certain fixed conditions as to temperature, length, volume, etc.; as, the coefficient of expansion; the coefficient of friction.
a.
Incapable of, or indisposed to, effective action; habitually slack or remiss; effecting little or nothing; as, inefficient workmen; an inefficient administrator.
a.
Strong; powerful; efficient.
n.
A dominating power.