Rapid growth of the complexity of a problem due to its combinatorial properties
This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Combinatorial explosion" – news · newspapers · books · scholar · JSTOR(September 2014) (Learn how and when to remove this message)
In mathematics, a combinatorial explosion is the rapid growth of the complexity of a problem due to how the combinatorics of the problem is affected by the input, constraints, and bounds of the problem. Combinatorial explosion is sometimes used to justify the intractability of certain problems.[1][2] Examples of such problems include certain mathematical functions, the analysis of some puzzles and games, and some pathological examples which can be modelled as the Ackermann function.
^Krippendorff, Klaus. "Combinatorial Explosion". Web Dictionary of Cybernetics and Systems. PRINCIPIA CYBERNETICA WEB. Archived from the original on 6 August 2010. Retrieved 29 November 2010.
^http://intelligence.worldofcomputing/combinatorial-explosion Archived 2011-08-23 at the Wayback Machine Combinatorial Explosion.
and 24 Related for: Combinatorial explosion information
In mathematics, a combinatorialexplosion is the rapid growth of the complexity of a problem due to how the combinatorics of the problem is affected by...
through the "maze" was simply astronomical (a situation known as a "combinatorialexplosion"). Researchers would reduce the search space by using heuristics...
described by William E. Combs in 1997. It is designed to prevent combinatorialexplosion in fuzzy logic rules. The Combs method takes advantage of the logical...
done in other sciences. He specifically mentioned the problem of "combinatorialexplosion" or "intractability", which implied that many of AI's most successful...
many aspects ("dimensions") Combinatorialexplosion – Rapid growth of the complexity of a problem due to its combinatorial properties Data mining – Process...
that will solve 9×9 puzzles (n = 9) in fractions of a second, but combinatorialexplosion occurs as n increases, creating limits to the properties of Sudokus...
depth searched or some type of average. Brute-force search CombinatorialexplosionCombinatorial optimization Search algorithm State space search Russell...
for solving large reasoning problems because they experience a "combinatorialexplosion": They become exponentially slower as the problems grow. Even humans...
stated that AI researchers had failed to address the issue of combinatorialexplosion when solving problems within real-world domains. That is, the report...
'digit-single'; originally called Number Place) is a logic-based, combinatorial number-placement puzzle. In classic Sudoku, the objective is to fill...
and can be re-used. This eliminates backtracking and prevents a combinatorialexplosion. Chart parsing is generally credited to Martin Kay. A common approach...
) {\displaystyle O(n^{4})} operations, but that does not take combinatorialexplosion into account. Burden & Faires 1993, p. 401. Gilbert Strang. "6:...
real-world problems because the search was easily lost in the combinatorialexplosion. Put another way, the number of "walks" through the inferential...
due to the exponentially increasing number of nodes, leading to combinatorialexplosion. For example, if the branching factor is 10, then there will be...
intelligence and remains an important method to overcome the intractable combinatorialexplosion of exponentially growing searches. List processing To implement...
refers to this principle as the span of managerial responsibility. Combinatorialexplosion in communication Interaction frequency Network theory Scientific...
Chess portal Solving chess Go and mathematics Game complexity Combinatorialexplosion Claude Shannon (1950). "Programming a Computer for Playing Chess"...
allows the parts of a protocol to be designed and tested without a combinatorialexplosion of cases, keeping each design relatively simple. The communication...
language P, then from P to B. Using a pivot language avoids the combinatorialexplosion of having translators across every combination of the supported...
computational problems, suffers from the curse of dimensionality and the combinatorialexplosion. An alternative language for describing planning problems is that...
combinatorics Burnside's lemma CombinatorialexplosionCombinatorial game theory Combinatorial principles Combinatorial species Inclusion–exclusion principle...
for general n 2 × n 2 {\displaystyle n^{2}\times n^{2}} grids. Combinatorialexplosion (with summary of grid count of Sudoku compared to Latin squares)...
Global Information