Polynomial-time approximation algorithms for weighted LCS problem

We consider a variant of the well-known Longest Common Subsequence (LCS) problem for weighted sequences. A weighted sequence determines the probability for each symbol to occur at a given position of the sequence (such sequences are also called Position Weighted Matrices, PWM). Two possible such ver...

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Vydáno v:Discrete Applied Mathematics Ročník 204; s. 38 - 48
Hlavní autoři: Cygan, M., Kubica, M., Radoszewski, J., Rytter, W., Waleń, T.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 11.05.2016
Témata:
Algorithms
Alphabets
Approximation
Longest common subsequence
Mathematical analysis
Matrices (mathematics)
Polynomial-time approximation scheme
Pulse duration modulation
Sequences
Symbols
Weighted sequence
Polynomial-time approximation scheme
Weighted sequence
Longest common subsequence
ISSN:0166-218X, 1872-6771
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Shrnutí:We consider a variant of the well-known Longest Common Subsequence (LCS) problem for weighted sequences. A weighted sequence determines the probability for each symbol to occur at a given position of the sequence (such sequences are also called Position Weighted Matrices, PWM). Two possible such versions of the problem were proposed by (Amir et al., 2009 and 2010), they are called LCWS and LCWS2 (Longest Common Weighted Subsequence 1 and 2). We solve an open problem, stated in the paper by Amir et al., of the tractability of a log-probability version of LCWS2 problem for bounded alphabets, showing that it is NP-hard already for an alphabet of size 2. We also improve the (1/|Σ|)-approximation algorithm given by Amir et al. (where Σ is the alphabet): we show a polynomial-time approximation scheme (PTAS) for the LCWS2 problem using O(n5) space. We also give a simpler (1/2)-approximation algorithm for the same problem using only O(n2) space.
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ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2015.11.011