Computer Science
In computer science, pathological has a slightly different sense with regard to the study of algorithms. Here, an input (or set of inputs) is said to be pathological if it causes atypical behavior from the algorithm, such as a violation of its average case complexity, or even its correctness. For example, hash tables generally have pathological inputs: sets of keys that collide on hash values. Quicksort normally has O(n log n) time complexity, but deteriorates to O(n2) when given input that triggers suboptimal behaviour.
The term is often used pejoratively, as a way of dismissing such inputs as being specially designed to break a routine that is otherwise sound in practice (compare with Byzantine). On the other hand, awareness of pathological inputs is important as they can be exploited to mount a denial-of-service attack on a computer system. Also, the term in this sense is a matter of subjective judgment as with its other senses. Given enough run time, a sufficiently large and diverse user community, or other factors, an input which may be dismissed as pathological could in fact occur (as seen in the first test flight of the Ariane 5).
Read more about this topic: Pathological (mathematics)
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