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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
Set preferred to any other by a majority
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 it ignores
Smith_set
Set of all Pareto efficient situations
(also called the Pareto front, Pareto set, Pareto boundary or Pareto curve) is the set of all Pareto efficient solutions. Informally, this means when
Pareto_frontier
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
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
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)
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
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
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
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)
In computational geometry, a point p in a finite set of points S is said to be maximal or non-dominated if there is no other point q in S whose coordinates
Maxima_of_a_point_set
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
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
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
Rajmohan Rajaraman, Torsten Suel, "An efficient distributed algorithm for constructing small dominating sets" Distributed Computing 15(3) pp. 193–205
Torsten_Suel
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)
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
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 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
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
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
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)
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
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
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
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
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)
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
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
2019 EF4 tornado in Kansas, U.S.
that UAVs have extra advantages than human-based surveyors, due to more efficient usages and costs. An example is that a UAV, with a mounted camera, is
2019_Linwood_tornado
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
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
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
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
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
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)
American football player (born 1994)
Following the loss to the Falcons, the Winston-led Buccaneers began playing efficient offense as well as exceptional defense and special teams play, resulting
Jameis_Winston
Pairing where no unchosen pair prefers each other over their choice
structure of a finite distributive lattice, and this structure leads to efficient algorithms for several problems on stable marriages. In a uniformly-random
Stable_matching_problem
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
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
American football player (born 1988)
starting quarterback over Joseph. Keenum's outstanding pocket presence and efficient passing won out in the end over Joseph's stronger arm and running ability
Case_Keenum
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
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)
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
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
Quality indicator for Pareto-front approximation sets
is dominated by an approximation set and bounded by a specified reference point. In earlier multi-objective optimization literature, the same set-quality
Hypervolume_indicator
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
American professional boxer (born 1994)
stats, Baumgardner outlanded Mayer in total punches 116 to 104, was more efficient in her output landing 35% of punches to Mayer's 29%, and connected with
Alycia_Baumgardner
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
Support for the Key Policies Within the "One Big Beautiful Bill"". co/efficient. June 2025. Retrieved August 5, 2025. "Clarity Omnibus Overview – March
2026_United_States_elections
Non-partisan network of interest groups in the field of EU politics in Germany
accumulated over 70 new memberships. To accommodate new members more efficiently, the Board of Directors now decides on the admission of new members.
European_Movement_Germany
Method for recursively subdividing a space into two subsets using hyperplanes
of Doom. In 1992, Teller's PhD thesis described the efficient generation of potentially visible sets as a pre-processing step to accelerate real-time visible
Binary_space_partitioning
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
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
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
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
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
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
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
Breadth of ideas which can be represented in a formal language
same set of strings is hard, while doing the same for arbitrary context-free grammars is completely impossible. However, it can still be efficiently decided
Expressive power (computer science)
Expressive_power_(computer_science)
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
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
insures that household goals are funded in an efficient manner. In goals-based investing, assets are the full set of resources the investor has available (including
Goal-based_investing
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)
American football tournament
points after a Texans turnover; however, Drake Maye played a far more efficient game than Stroud, throwing three touchdown passes and one interception
2025–26_NFL_playoffs
Sequence of operations for a task
mathematics and computer science, an algorithm (/ˈælɡərɪðəm/ ) is any well-defined set of instructions that when followed terminates after a finite number of steps
Algorithm
2023 film by Jonathan Glazer
the phone that he spent his time at the party thinking about the most efficient way to gas the attendees. As Höss leaves his Berlin office and descends
The_Zone_of_Interest_(film)
the main themes is the comparison between a corrupt democracy and an efficient dictatorship and the moral issues of such a situation, with Yang Wen-li
List of Legend of the Galactic Heroes episodes
List_of_Legend_of_the_Galactic_Heroes_episodes
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
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
graphs. Edge dominating set, dominating set, r-dominating set, connected dominating set, r-scattered set, minimum maximal matching, independent set, maximum
Bidimensionality
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
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)
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
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)
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)
2024 animated Disney film
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
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)
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
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
System that transfers heat from one space to another
conditioner. 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
Bale Dalton in FL-07". Blue Dog PAC. June 10, 2026. "Sherrill unveils first set of midterm endorsements". Retrieved August 7, 2026. Ogles, Jacob (December
2026 United States House of Representatives elections in Florida
2026_United_States_House_of_Representatives_elections_in_Florida
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
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
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
Vivienne; Chen, Yu-Hsin; Yang, Tien-Ju; Emer, Joel S. (2017-11-20). "Efficient Processing of Deep Neural Networks: A Tutorial and Survey". Proceedings
Hardware/software_co-design
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
Sultan of Delhi from 1296 to 1316
requirements." To enforce these land and agrarian reforms, Alauddin set up a strong and efficient revenue administration system. His government recruited many
Alauddin_Khalji
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
Computer bus interface for storage devices
swapping, faster data transfer through higher signaling rates, and more efficient transfer through an (optional) I/O queuing protocol. Serial ATA industry
SATA
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)
American basketball player (born 2002)
August 20th against Los Angeles Sparks, going 9 for 9. She had the most efficient 20-10 game in history, in addition to 8 assists and 3 steals. On August
Angel_Reese
Family of instruction set architectures
to the CPU's native VLIW instruction set. Transmeta argued that their approach allows for more power efficient designs since the CPU can forgo the complicated
X86
Algorithms which recursively solve subproblems
used in some efficient FFT implementations, where the base cases are unrolled implementations of divide-and-conquer FFT algorithms for a set of fixed sizes
Divide-and-conquer_algorithm
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)
travel, tourism, insurance
EFFICIENT DOMINATING-SET
EFFICIENT DOMINATING-SET
EFFICIENT DOMINATING-SET
EFFICIENT DOMINATING-SET
EFFICIENT DOMINATING-SET
EFFICIENT DOMINATING-SET
EFFICIENT DOMINATING-SET
EFFICIENT DOMINATING-SET
EFFICIENT DOMINATING-SET
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