On the parameterized complexity of the fixed alphabet shortest common supersequence and longest common subsequence problems
✍ Scribed by Krzysztof Pietrzak
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 205 KB
- Volume
- 67
- Category
- Article
- ISSN
- 0022-0000
No coin nor oath required. For personal study only.
✦ Synopsis
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 problems. Here n is the size of the problem instance, a is constant, k is the number of strings and f is any function of k: The fixed alphabet version of the LCS problem is of particular interest considering the importance of sequence comparison (e.g. multiple sequence alignment) in the fixed length alphabet world of DNA and protein sequences.