# COMPUTATIONALComplexity

**DOI:**https://doi.org/10.1007/1-4020-0611-X_141

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The term “computational complexity” has two usages which must be distinguished. On the one hand, it refers to an *algorithm* for solving instances of a *problem*: broadly stated, the computational complexity of an algorithm is a measure of how many steps the algorithm will require in the worst case for an instance or input of a given size. The number of steps is measured as a function of that size.

The term's second, more important use is in reference to a problem itself. The theory of computational complexity involves classifying problems according to their inherent tractability or intractability — that is, whether they are “easy” or “hard” to solve. This classification scheme includes the well-known classes *P* and *NP*; the terms “*NP*-complete” and “*NP*-hard” are related to the class *NP*.

## ALGORITHMS AND COMPLEXITY

To understand what is meant by the complexity of an algorithm, we must define algorithms, problems, and problem instances. Moreover, we must understand how one measures the size of a...

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