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We study the complexity of the problem of searching for a set of patternsthat separate two given sets of strings. This problem has applications in awide variety of areas, most notably in data mining, computational biology, andin understanding the complexity of genetic algorithms. We show that the basicproblem of finding a small set of patterns that match one set of strings but donot match any string in a second set is difficult (NP-complete, W[2]-hard whenparameterized by the size of the pattern set, and APX-hard). We then perform adetailed parameterized analysis of the problem, separating tractable andintractable variants. In particular we show that parameterizing by the size ofpattern set and the number of strings, and the size of the alphabet and thenumber of strings give FPT results, amongst others.

Separating Sets of Strings by Finding Matching Patterns is Almost Always Hard