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# Complexity

[kuh m-plek-si-tee] /kəmˈplɛk sɪ ti/

noun, plural complexities for 2.
1.
the state or quality of being ; intricacy:
the complexity of urban life.
2.
something :
the complexities of foreign policy.
/kəmˈplɛksɪtɪ/
noun (pl) -ties
1.
the state or quality of being intricate or complex
2.
something intricate or complex; complication
n.

1721, “composite nature,” from complex (adj.) + -ity. Meaning “intricacy” is from 1790. Meaning “a complex condition” is from 1794.

algorithm
The level in difficulty in solving mathematically posed problems as measured by the time, number of steps or arithmetic operations, or memory space required (called time complexity, computational complexity, and space complexity, respectively).
The interesting aspect is usually how complexity scales with the size of the input (the “scalability”), where the size of the input is described by some number N. Thus an algorithm may have computational complexity O(N^2) (of the order of the square of the size of the input), in which case if the input doubles in size, the computation will take four times as many steps. The ideal is a constant time algorithm (O(1)) or failing that, O(N).
(1994-10-20)

Tagged:

• Complexity analysis

In sructured program design, a quality-control operation that counts the number of “compares” in the logic implementing a function; a value of less than 10 is considered acceptable.

• Complexity class

algorithm A collection of algorithms or computable functions with the same complexity. (1996-04-24)

• Complexity measure

algorithm A quantity describing the complexity of a computation. (1996-04-24)

• Complexity-theory

noun 1. the study of complex and chaotic systems and how order, pattern, and structure can arise from them. 2. the theory that processes having a large number of seemingly independent agents can spontaneously order themselves into a coherent system. noun 1. (maths) the study of complex systems, including subjects such as chaos theory and […]

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