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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
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
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
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
Focal_point_(game_theory)
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
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
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
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
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
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
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
Concept in conflict studies
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Conflict_escalation
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
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
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
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
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
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
Economic phenomenon
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Tyranny_of_small_decisions
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
List_of_games_in_game_theory
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
Concept in game theory
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Incentive_compatibility
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
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
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
Game theory scenario
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Win–win_game
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)
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
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
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
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
Concept in game theory
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Shapley_value
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)
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
depth searched or some type of average. Brute-force search Combinatorial explosion Combinatorial optimization Search algorithm State space search Russell
Combinatorial_search
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
Experimental tool
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Dictator_game
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
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
Trigger strategy
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Grim_trigger
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)
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
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
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
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
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
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)
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
Solution concept in Game Theory
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Cursed_equilibrium
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 theory concept
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Subgame_perfect_equilibrium
Incomplete-information coordination game
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Electronic_mail_game
Term in business management
refers to this principle as the span of managerial responsibility. Combinatorial explosion in communication Interaction frequency Network theory Scientific
Span_of_control
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
Problem in game theory
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
El_Farol_Bar_problem
Simultaneous game found in game theory
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Coordination_game
Hand game for two or more players
turns tapping one hand against another. Chopsticks is an example of a combinatorial game, and is solved in the sense that, with perfect play, an optimal
Chopsticks_(hand_game)
Military strategy during the Cold War with regard to the use of nuclear weapons
nuclear close calls can be defined as instances in which unwanted nuclear explosions were avoided either 'independently' of control practices, 'despite' control
Deterrence_theory
Solution concept in Game Theory
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Bayes_correlated_equilibrium
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
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
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
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
Economic model of competition
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Bertrand_competition
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
Decrease in severity of conflicts
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
De-escalation
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)
Game theory model of aggression
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
War_of_attrition_(game)
Topics referred to by the same term
Coast to Coast Search for "explosion" , "explosive", "explode", "exploded", or "exploder" on Wikipedia. Combinatorial explosion, in mathematics, the effect
Explosion_(disambiguation)
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)
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
Game in economic experiments
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Ultimatum_game
Diplomatic policy of concessions
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Appeasement
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Fictitious_play
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
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
Growth of quantities at rate proportional to the current amount
growth Cell growth Combinatorial explosion Exponential algorithm EXPSPACE EXPTIME Hausdorff dimension Hyperbolic growth Information explosion Law of accelerating
Exponential_growth
Game theory concept
Scotchmer Thomas Schelling William Vickrey Combinatorial game theory Core concepts Combinatorial explosion Determinacy Disjunctive sum First-player and
Bayesian_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
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
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
COMBINATORIAL EXPLOSION
COMBINATORIAL EXPLOSION
COMBINATORIAL EXPLOSION
COMBINATORIAL EXPLOSION
Boy/Male
Hindu
First Ray of sunlight, Vishnus Ansh
Male
Native American
Native American Cheyenne name HOTUAEKHAASHTAIT means "tall bull."
Boy/Male
Latin Russian
Attendant.
Girl/Female
Arabic, Muslim
Acquirer; Obtainer; One who Succeeds; Winner
Boy/Male
Indian
Servant
Girl/Female
Indian
Star
Boy/Male
Irish
Holy.
Girl/Female
Muslim
Intelligent, Pure
Surname or Lastname
North German and Dutch
North German and Dutch : variant of Hopp.South German : nickname from dialect hoppen ‘to hop’ (a variant of standard German hüpfen).Danish : from North German Hopp (see Hopf), or the Danish byname Hoppe ‘horse’, ‘mare’.English : metonymic form of Hopper 1.
Boy/Male
Hindu
Lord Shiva
COMBINATORIAL EXPLOSION
COMBINATORIAL EXPLOSION
COMBINATORIAL EXPLOSION
COMBINATORIAL EXPLOSION
COMBINATORIAL EXPLOSION
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 contrivance or apparatus to prevent the explosion of steam boilers.
n.
An instrument or agent causing explosion; an exploder; also, an explosive.
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.
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.
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.
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 bursting open, as of a steam boiler, in a less sudden manner than by explosion. See Explosion.
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.
a.
Driving or bursting out with violence and noise; causing explosion; as, the explosive force of gunpowder.
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.
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 violent outburst of feeling, manifested by excited language, action, etc.; as, an explosion of wrath.
v. t.
To clean, as the inside of a cannon, by the explosion of a small quantity of powder.
n.
An explosion, or the noise of one.
n.
A bursting with violence and loud noise, because of internal pressure; as, the explosion of a gun, a bomb, a steam boiler, etc.
v. t.
To burst, shatter, or destroy by an explosion; -- usually with up, down, open, or similar adverb; as, to blow up a building.
n.
A burstion inwards, as of a vessel from which the air has been exhausted; -- contrasted with 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.