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Rapid growth of the complexity of a problem due to its combinatorial properties
In mathematics, a combinatorial explosion is the rapid growth of the complexity of a problem due to the way its combinatorics depends on input, constraints
Combinatorial_explosion
paths through the "maze" was astronomical (a situation known as a "combinatorial explosion"). Researchers would reduce the search space by using heuristics
History of artificial intelligence
History_of_artificial_intelligence
Branch of game theory about two-player sequential games with perfect information
Combinatorial game theory is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information
Combinatorial_game_theory
Problem-solving technique and algorithmic paradigm
tends to grow very quickly as the size of the problem increases (§Combinatorial explosion). Therefore, brute-force search is typically used when the problem
Brute-force_search
1973 article on artificial intelligence research
stated that AI researchers had failed to address the issue of combinatorial explosion when solving problems within real-world domains. That is, the report
Lighthill_report
described by William E. Combs in 1997. It is designed to prevent combinatorial explosion in fuzzy logic rules. The Combs method takes advantage of the logical
Combs_method
Logical paradox in decision-making theory
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Paradox_of_tolerance
Solution concept of a non-cooperative game
Jack; Fulkerson, Delbert Ray (1970). "Bottleneck extrema". Journal of Combinatorial Theory. 8 (3): 299–306. doi:10.1016/S0021-9800(70)80083-7. Gurvich,
Nash_equilibrium
depth searched or some type of average. Brute-force search Combinatorial explosion Combinatorial optimization Search algorithm State space search Russell
Combinatorial_search
Area of combinatorics that deals with the number of ways certain patterns can be formed
combinatorics Burnside's lemma Combinatorial explosion Combinatorial game theory Combinatorial principles Combinatorial species Inclusion–exclusion principle
Enumerative_combinatorics
Category of sales software
so on. If the product is highly configurable, the user may face combinatorial explosion, which means the rapid growth of the complexity of a problem. Thus
Configure,_price_and_quote
Rapid increase in the amount of published information or data
many aspects ("dimensions") Combinatorial explosion – Rapid growth of the complexity of a problem due to its combinatorial properties Data mining – Process
Information_explosion
Algorithms to complete a sudoku
that will solve 9×9 puzzles (n = 9) in fractions of a second, but combinatorial explosion occurs as n increases, creating limits to the properties of Sudokus
Sudoku_solving_algorithms
Intelligence of machines
for solving large reasoning problems because they experience a "combinatorial explosion": They become exponentially slower as the problems grow. Even humans
Artificial_intelligence
Paper-and-pencil game for two players
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Tic-tac-toe
Standard example in game theory
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Prisoner's_dilemma
Mathematical models of strategic interactions
called combinatorial games. Examples include chess, shogi, and Go. Games that involve imperfect information may also have a strong combinatorial character
Game_theory
Inference rule in logic, proof theory, and automated theorem proving
trying all ground instances of the given formula. This source of combinatorial explosion was eliminated in 1965 by John Alan Robinson's syntactical unification
Resolution_(logic)
Overuse of a shared resource
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Tragedy_of_the_commons
Period of reduced funding and interest in AI research
done in other sciences. He specifically mentioned the problem of "combinatorial explosion" or "intractability", which implied that many of AI's most successful
AI_winter
Situation where total gains match total losses
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Zero-sum_game
Hungarian and American mathematician and physicist (1903–1957)
structure of any new mathematical theory; An intuitive feeling for the combinatorial superstructure of new theories. Although he was commonly described as
John_von_Neumann
Decision rule used for minimizing the possible loss for a worst-case scenario
is a decision rule used in artificial intelligence, decision theory, combinatorial game theory, statistics, and philosophy for minimizing the possible
Minimax
Israeli-American psychologist and economist (1934–2024)
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Daniel_Kahneman
Level of information in economics and game theory
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Complete_information
Concept in game theory
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Shapley_value
English saying meaning "equivalent retaliation"
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Tit_for_tat
Pairing where no unchosen pair prefers each other over their choice
Machine. Knuth, D. E. (1996). Stable Marriage and Its Relation to Other Combinatorial Problems: An Introduction to the Mathematical Analysis of Algorithms
Stable_matching_problem
Facilitating a peaceful outcome to a dispute
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Conflict_resolution
Hand game for two players or more
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Rock_paper_scissors
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
List_of_games_in_game_theory
Condition in economics and game theory
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Perfect_information
Concept in conflict studies
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Conflict_escalation
Logic-based number-placement puzzle
'digit-single'; originally called Number Place) is a logic-based, combinatorial number-placement puzzle. In classic Sudoku, the objective is to fill
Sudoku
Problem in process of sharing surplus
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Cooperative_bargaining
Game whose outcome can be correctly predicted
full information and no element of chance; solving such a game may use combinatorial game theory or computer assistance. A two-player game can be solved
Solved_game
Finding an optimal algorithm for playing chess
It is also related to more generally solving chess-like games (i.e. combinatorial games of perfect information) such as Capablanca chess and infinite
Solving_chess
Political model of international conflict resolution
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Two-level_game_theory
Simple mathematical game
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Pirate_game
Tendency to overestimate in auctions
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Winner's_curse
Two-player coordination game in game theory
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Battle of the sexes (game theory)
Battle_of_the_sexes_(game_theory)
Overview of and topical guide to combinatorics
Steinhaus polygon notation Large number effects Exponential growth Combinatorial explosion Branching factor Granularity Curse of dimensionality Concentration
Outline_of_combinatorics
Estimate of number of possible chess games
length of 80 plies (or, equivalently, 40 moves). Chess portal Combinatorial explosion Game complexity Go and mathematics Solving chess Shannon, Claude
Shannon_number
Conflict between safety and cooperation
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Stag_hunt
Game theory scenario
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Win–win_game
Situation where all parties are worse off
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
No-win_situation
Poker game developed by Harold Kuhn
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Kuhn_poker
Proof all ranked voting rules have spoilers
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Arrow's_impossibility_theorem
Cooperation between firms to limit competition
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Collusion
Complete plan on how a game player will behave in every possible game situation
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Strategy_(game_theory)
Israeli psychologist (1937–1996)
and covered him with his body. Tversky was wounded by shrapnel from the explosion, which remained in his body for the rest of his life. The soldier he saved
Amos_Tversky
Human behavior pattern in which the participant takes on increasing risk
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Escalation_of_commitment
Model of humans as rational, self-interested agents
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Homo_economicus
Computer program created in 1959
real-world problems because the search was easily lost in the combinatorial explosion. Put another way, the number of "walks" through the inferential
General_Problem_Solver
Game where a certain player can force a win with perfect play
In combinatorial game theory, a two-player deterministic perfect information turn-based game is a first-player win if with perfect play the first player
First-player and second-player win
First-player_and_second-player_win
Solution concept in game theory
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Evolutionarily stable strategy
Evolutionarily_stable_strategy
Computational problem in graph theory
dimension number increases and the search space suffers a serious combinatorial explosion. Some techniques for determining the upper and lower bounds for
Snake-in-the-box
Concept in game theory
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Focal_point_(game_theory)
Weakly optimal allocation of resources
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Pareto_efficiency
Diplomatic policy of concessions
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Appeasement
Representation of a game in game theory
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Normal-form_game
Theorem in game theory
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Aumann's_agreement_theorem
Statement that players know and also know that other players know (ad infinitum)
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Common_knowledge_(logic)
Concept in economics and game theory
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Price_of_anarchy
Model of conflict for two players in game theory
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Chicken_(game)
Making of satisfactory, not optimal, decisions
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Bounded_rationality
Game illustrating paradox in rational choice theory
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Dollar_auction
System for exchanging messages between computing systems
allows the parts of a protocol to be designed and tested without a combinatorial explosion of cases, keeping each design relatively simple. The communication
Communication_protocol
Type of parser for ambiguous grammars
and can be re-used. This eliminates backtracking and prevents a combinatorial explosion. Chart parsing is generally credited to Martin Kay. A common approach
Chart_parser
Game in economic experiments
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Ultimatum_game
Economic model of competition
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Bertrand_competition
In board games that cannot end in a draw, one of the two players has a winning strategy
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Zermelo's theorem (game theory)
Zermelo's_theorem_(game_theory)
Class of games where players choose their actions sequentially
perfect information—where all prior moves are known—can be analyzed using combinatorial game theory, a mathematical approach to strategic decision-making. In
Sequential_game
Study of strategic decision making
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Mean-field_game_theory
Search algorithm
adversarial search algorithm used commonly for machine playing of two-player combinatorial games (Tic-tac-toe, Chess, Connect 4, etc.). It stops evaluating a move
Alpha–beta_pruning
Software project management principle
Communication overhead increases as the number of people increases. Due to combinatorial explosion, the number of different communication channels increases rapidly
Brooks's_law
1956 computer program written by Allen Newell, Herbert A. Simon and Cliff Shaw
intelligence and remains an important method to overcome the intractable combinatorial explosion of exponentially growing searches. List processing To implement
Logic_Theorist
Preference of known risks to unknown risks
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Ambiguity_aversion
Difficulties arising when analyzing data with many aspects ("dimensions")
of values must be considered. This effect is also known as the combinatorial explosion. Even in the simplest case of d {\displaystyle d} binary variables
Curse_of_dimensionality
Game where groups of players may enforce cooperative behaviour
\pi } . Submodular and supermodular set functions are also studied in combinatorial optimization. Many of the results in (Shapley 1971) have analogues in
Cooperative_game_theory
Resource distribution game
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Blotto_game
Field of economics and game theory
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Mechanism_design
Intermediary language between different languages
language P, then from P to B. Using a pivot language avoids the combinatorial explosion of having translators across every combination of the supported
Pivot_language
Dynamical system
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Replicator_equation
Field in social science
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Peace_and_conflict_studies
Experimental tool
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Dictator_game
Simple game studied in game theory
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Matching_pennies
Type of regression analysis
geneticengine (Genetic Engine) Most symbolic regression algorithms prevent combinatorial explosion by implementing evolutionary algorithms that iteratively improve
Symbolic_regression
Concept in artificial intelligence research
classical AI technologies started to face intractable issues (e.g. combinatorial explosion) when confronted with real-world modeling problems. All approaches
Situated approach (artificial intelligence)
Situated_approach_(artificial_intelligence)
Economic phenomenon
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Tyranny_of_small_decisions
Inherent flaw in computer instructions
for anything but the shortest programs, because of problems of combinatorial explosion and indeterminacy. One goal of software testing is to find bugs
Software_bug
Mathematical game
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Guess_2/3_of_the_average
Quality of a strategy in game theory
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Strategic_dominance
Game-theoretic concept
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Cheap_talk
Economic model
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Cournot_competition
Solution to the fair division problem
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Moving-knife_procedure
Hungarian-American economist and philosopher (1920–2000)
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
John_Harsanyi
Game theory concept
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Subgame_perfect_equilibrium
Principle in economics and game theory
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Revelation_principle
Process of reasoning backwards in sequence
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Backward_induction
COMBINATORIAL EXPLOSION
COMBINATORIAL EXPLOSION
COMBINATORIAL EXPLOSION
COMBINATORIAL EXPLOSION
Boy/Male
Arabic
Servant of the capable.
Male
English
English form of French Gérald, GERALD means "spear ruler."
Boy/Male
Hindu
Lord Ram and seetha
Girl/Female
Indian
Fearless
Girl/Female
Indian, Sikh
Queen; Friend
Boy/Male
Indian, Sanskrit
Highly Controlled
Boy/Male
Indian, Sanskrit
Health
Boy/Male
Indian
Favor, Grace, Kindness
Girl/Female
Tamil
Kanmani | கநà¯à®®à®¾à®¨à¯€
Precious like An eye
Girl/Female
Irish
Loved one.
COMBINATORIAL EXPLOSION
COMBINATORIAL EXPLOSION
COMBINATORIAL EXPLOSION
COMBINATORIAL EXPLOSION
COMBINATORIAL EXPLOSION
n.
A radioactive isotope of strontium produced by certain nuclear reactions, and constituting one of the prominent harmful components of radioactive fallout from nuclear explosions; also called radiostrontium. It has a half-life of 28 years.
n.
A violent outburst of feeling, manifested by excited language, action, etc.; as, an explosion of wrath.
v. t.
In blasting, to plug up with clay, earth, dry sand, sod, or other material, as a hole bored in a rock, in order to prevent the force of the explosion from being misdirected.
n.
A burstion inwards, as of a vessel from which the air has been exhausted; -- contrasted with explosion.
n.
A contrivance or apparatus to prevent the explosion of steam boilers.
n.
An instrument or agent causing explosion; an exploder; also, an explosive.
n.
An explosion, or the noise of one.
n.
The act of rending, or attempting to rend, heavy masses of rock, earth, etc., by the explosion of gunpowder, dynamite, etc.; also, the charge used for this purpose.
v. t.
To clean, as the inside of a cannon, by the explosion of a small quantity of powder.
v. t.
To burst, shatter, or destroy by an explosion; -- usually with up, down, open, or similar adverb; as, to blow up a building.
a.
Driving or bursting out with violence and noise; causing explosion; as, the explosive force of gunpowder.
v. t.
To break at once into many pieces; to dash, burst, or part violently into fragments; to rend into splinters; as, an explosion shatters a rock or a bomb; too much steam shatters a boiler; an oak is shattered by lightning.
n.
A sudden breaking forth; a violent rending; an explosion; as, a burst of thunder; a burst of applause; a burst of passion; a burst of inspiration.
n.
A bursting with violence and loud noise, because of internal pressure; as, the explosion of a gun, a bomb, a steam boiler, etc.
n.
The act of exploding; detonation; a chemical action which causes the sudden formation of a great volume of expanded gas; as, the explosion of gunpowder, of fire damp,etc.
n.
A weapon which throws or propels a missile to a distance; any firearm or instrument for throwing projectiles by the explosion of gunpowder, consisting of a tube or barrel closed at one end, in which the projectile is placed, with an explosive charge behind, which is ignited by various means. Muskets, rifles, carbines, and fowling pieces are smaller guns, for hand use, and are called small arms. Larger guns are called cannon, ordnance, fieldpieces, carronades, howitzers, etc. See these terms in the Vocabulary.
n.
A ball filled with powder or other combustibles, intended to be thrown among enemies, and to injure by explosion; also, to set fire to their works and light them up, so that movements may be seen.
n.
A bursting open, as of a steam boiler, in a less sudden manner than by explosion. See Explosion.
n.
A puff, as of smoke from a pipe, or of dust from a puffball; a slight explosion, as of a small quantity of gunpowder.