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Consistent subsequences and supersequences

✍ Scribed by Campbell Fraser

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
899 KB
Volume
165
Category
Article
ISSN
0304-3975

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In the paper two combinatorial problems for the set F n q of sequences of length n over the alphabet F q =[0, 1, ..., q&1] are considered. The maximum size N & q (n, t) of the set of common subsequences of length n&t and the maximum size N + q (n, t) of the set of common supersequences of length n+t

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We show that the fixed alphabet shortest common supersequence (SCS) and the fixed alphabet longest common subsequence (LCS) problems parameterized in the number of strings are W ½1-hard. Unless W ½1 ¼ FPT; this rules out the existence of algorithms with time complexity of Oð f ðkÞn a Þ for those pro