Separating sets of strings by finding matching patterns is almost always hard

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• 作者：Giuseppe Lancia^a ; Luke Mathieson^b ; ^{luke.mathieson@newcastle.edu.au} ; Pablo Moscato^b
• 关键词：Pattern identification ; Parameterized complexity ; Computational complexity
• 刊名：Theoretical Computer Science
• 出版年：2017
• 出版时间：22 February 2017
• 年：2017
• 卷：665
• 期：Complete
• 页码：73-86
• 全文大小：483 K
• 卷排序：665

文摘

We study the complexity of the problem of searching for a set of patterns that separate two given sets of strings. This problem has applications in a wide variety of areas, most notably in data mining, computational biology, and in understanding the complexity of genetic algorithms. We show that the basic problem of finding a small set of patterns that match one set of strings but do not match any string in a second set is difficult (NP-complete, W[2]W[2]-hard when parameterized by the size of the pattern set, and APXAPX-hard). We then perform a detailed parameterized analysis of the problem, separating tractable and intractable variants. In particular we show that parameterizing by the size of pattern set and the number of strings, and the size of the alphabet and the number of strings give FPTFPT results, amongst others.