On a cyclic string-to-string correction problem
Information Processing Letters
More on the complexity of common superstring and supersequence problems
Theoretical Computer Science
The parameterized complexity of sequence alignment and consensus
Theoretical Computer Science
On the Approximation of Shortest Common Supersequencesand Longest Common Subsequences
SIAM Journal on Computing
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
SIAM Journal on Computing
Algorithms for the Longest Common Subsequence Problem
Journal of the ACM (JACM)
The Complexity of Some Problems on Subsequences and Supersequences
Journal of the ACM (JACM)
Introduction to Algorithms
Towards optimal lower bounds for clique and chromatic number
Theoretical Computer Science
Fast Cyclic Edit Distance Computation with Weighted Edit Costs in Classification
ICPR '02 Proceedings of the 16 th International Conference on Pattern Recognition (ICPR'02) Volume 4 - Volume 4
A Subquadratic Sequence Alignment Algorithm for Unrestricted Scoring Matrices
SIAM Journal on Computing
Approximate coloring of uniform hypergraphs
Journal of Algorithms
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
Parameterized Complexity
Hi-index | 5.23 |
Given a finite set of strings X, the Longest Common Subsequence problem (LCS) consists in finding a subsequence common to all strings in X that is of maximal length. LCS is a central problem in stringology and finds broad applications in text compression, conception of error-detecting codes, or biological sequence comparison. However, in numerous contexts, words represent cyclic or unoriented sequences of symbols and LCS must be generalized to consider both orientations and/or all cyclic shifts of the strings involved. This occurs especially in computational biology when genetic material is sequenced from circular DNA or RNA molecules. In this work, we define three variants of LCS when the input words are unoriented and/or cyclic. We show that these problems are NP-hard, and W[1]-hard if parameterized in the number of input strings. These results still hold even if the three LCS variants are restricted to input languages over a binary alphabet. We also settle the parameterized complexity of our problems for most relevant parameters. Moreover, we study the approximability of these problems: we discuss the existence of approximation bounds depending on the cardinality of the alphabet, on the length of the shortest sequence, and on the number of input sequences. For this we prove that Maximum Independent Set in r-uniform hypergraphs is W[1]-hard if parameterized in the cardinality of the sought independent set and at least as hard to approximate as Maximum Independent Set in graphs.