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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
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
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
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)
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
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
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)
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
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
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
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
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
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
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)
conjecture: Does there exist a graph G {\displaystyle G} such that the dominating number, eternal domination number, and clique covering number satisfy
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
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
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
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
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
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
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
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
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
whose entries alternate in a prescribed way. In particular, if the vertex set of the graph is V, one should be able to choose a word w over the alphabet
Word-representable_graph
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
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
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)
Rajmohan Rajaraman, Torsten Suel, "An efficient distributed algorithm for constructing small dominating sets" Distributed Computing 15(3) pp. 193–205
Torsten_Suel
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
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
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
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)
graphs. Edge dominating set, dominating set, r-dominating set, connected dominating set, r-scattered set, minimum maximal matching, independent set, maximum
Bidimensionality
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)
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
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)
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
Fictional universe created by Isaac Asimov
series written by American author Isaac Asimov. The Foundation series is set in the same universe as Asimov's first published novel, Pebble in the Sky
Foundation_universe
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
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
History and future of the universe
the plasma became dilute enough so that neutrinos ceased interacting efficiently with the other particles and instead started free streaming through the
Chronology_of_the_universe
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
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
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
Details of the Dune science fiction novels
whose power is secured by his control of the Sardaukar, his brutally efficient military force. Imperial power is balanced by the assembly of noble houses
Organizations of the Dune universe
Organizations_of_the_Dune_universe
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
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
Mutant comic book character
especially women. Fueled by the betrayal, Nord became one of Germany's most efficient covert operatives. In the 1960s, his exploits attract the attention of
David_North_(character)
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
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
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
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
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
2023 superhero film by Andy Muschietti
for half a day in January 2023, in what was described as a "quick and efficient shoot". Miller received advice from Clooney on handling publicity and
The_Flash_(film)
Type of machine learning model
and laying on a exercise ball. The man... demonstrates how to increase efficient exercise work by running up and down balls. moves all his arms and legs
Large_language_model
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
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
8-speed automatic from 2008
March 2014. Retrieved 7 July 2019. 2nd generation and 3rd generation "Efficient And Dynamic · ZF Gearbox Brochure" (PDF). 1 September 2017. Archived from
ZF_8HP_transmission
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
French writer (1850–1893)
stories are characterized by economy of style and efficient, seemingly effortless dénouements. Many are set during the Franco-Prussian War of the 1870s, describing
Guy_de_Maupassant
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
mathematics, linguistics, and computer science—for the purpose of designing efficient and reliable data transmission methods. This typically involves the removal
Glossary_of_computer_science
US-based software and services company
Liy, Macarena Vidal (March 8, 2025). "Palantir, Trump's 'big brother' dominating the stock market". El País English. Au-Yeung, Angel (September 30, 2020)
Palantir
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
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)
Human-caused changes to climate on Earth
sector. In the transport sector, passengers and freight can switch to more efficient travel modes, such as buses and trains, or use electric vehicles. Industrial
Climate_change
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
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
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)
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
Scheduled passenger air journeys
Buenos Aires, with a flight time of 13 hours. The arrival of the more fuel-efficient turbofans made easier the possibility of longer flights. April 26, 1976 (1976-04-26):
Longest_flights
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
Japanese manga series by Tatsuki Fujimoto
(September–December) in the United States, and it was also the third "most efficient manga franchise" for retailer bookshelves, based on the website's calculations
Chainsaw_Man
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
German politician (1890–1945)
and the DAF became little more than an arm of the state for the more efficient deployment and disciplining of labour to serve the needs of the regime
Robert_Ley
2016 Indian film by Abhishek Kapoor
gorgeous, but opulence takes over substance – chinars, minars and lace dominating grip, passion and pace. For a love story, Fitoor lacks heat – you wish
Fitoor
Non-parametric classification method
Sridhar; Rastogi, Rajeev; Shim, Kyuseok (2000). "Efficient algorithms for mining outliers from large data sets". Proceedings of the 2000 ACM SIGMOD international
K-nearest_neighbors_algorithm
Ethnic cleansing of Palestinians
partitioning of post-Mandate Palestine neutralized the Arab Legion, Jordan's efficient, British-led army, which confined its activity to the area around Jerusalem
Nakba
Annual conference series on algorithms
ESA 1994 Sudipto Guha, Samir Khuller: Approximation Algorithms for Connected Dominating Sets. In ESA 1996 Jan van Leeuwen, Kurt Mehlhorn, Mike Paterson
European Symposium on Algorithms
European_Symposium_on_Algorithms
2003 novel by Marshall Brain
point of slavery, while humans in the utopian society more directly and efficiently participate in the management of the society as a whole and most or all
Manna_(novel)
City in California, United States
vapor street lamps. In 1978, the city decided to replace them with more efficient sodium vapor lamps. This triggered an outcry from astronomers at Palomar
San_Diego
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
1996 novel by David Foster Wallace
Odyssey, wherein the son Telemachus (Hal) has to grow apart from his dominating mother Penelope (Avril) and discover the truth about his absent father
Infinite_Jest
1985 Japanese film by Akira Kurosawa
suggests how wild and savage a journey it has been. At the start, this bold, dominating figure, now called Hidetora, is a sacred monster who wants to be a sort
Ran_(film)
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)
2012 Microsoft operating system version
Windows 8–based products under government contracts requiring "energy-efficient" devices. The Xinhua News Agency claimed that Windows 8 was being banned
Windows_8
2025 film by James Cameron
said that Chaplin was able to express Varang's fury, sexuality, and "dominating psychology" better than other candidates for the role. In January 2018
Avatar:_Fire_and_Ash
American reality television series
equipment in favor of a different mining set-up known as a de-rocker, in an attempt to process dirt more efficiently than the Hoffman's were able to last
Gold_Rush_(TV_series)
American science fiction media franchise
known universe for millennia by controlling the Sardaukar, a brutally efficient military force. Ten thousand years later, Imperial power is balanced by
Dune_(franchise)
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)
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
Track and field event
to dominate women's high jump for about 10 years until her retirement in 1967. Another American, George Horine, developed an even more efficient technique
High_jump
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