Trapezoid graphs and their coloring
Discrete Applied Mathematics
Simple fast algorithms for the editing distance between trees and related problems
SIAM Journal on Computing
On powers of m-trapezoid graphs
Discrete Applied Mathematics
Trapezoid graphs and generalizations, geometry and algorithms
Discrete Applied Mathematics
The longest common subsequence problem for sequences with nested arc annotations
Journal of Computer and System Sciences - Computational biology 2002
Pattern Matching for Arc-Annotated Sequences
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
On the computational complexity of 2-interval pattern matching problems
Theoretical Computer Science
Multiple genome alignment: chaining algorithms revisited
CPM'03 Proceedings of the 14th annual conference on Combinatorial pattern matching
RNA multiple structural alignment with longest common subsequences
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Consensus folding of unaligned RNA sequences revisited
RECOMB'05 Proceedings of the 9th Annual international conference on Research in Computational Molecular Biology
Comparing RNA structures: towards an intermediate model between the edit and the LAPCS problems
BSB'07 Proceedings of the 2nd Brazilian conference on Advances in bioinformatics and computational biology
Finding common structured patterns in linear graphs
Theoretical Computer Science
Common structured patterns in linear graphs: approximation and combinatorics
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
Longest common separable pattern among permutations
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
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In the context of non-coding RNA (ncRNA) multiple structural alignment, Davydov and Batzoglou introduced in [7] the problem of finding the largest nested linear graph that occurs in a set ${\mathcal{G}}$ of linear graphs, the so-called Max-NLS problem. This problem generalizes both the longest common subsequence problem and the maximum common homeomorphic subtree problem for rooted ordered trees. In the present paper, we give a fast algorithm for finding the largest nested linear subgraph of a linear graph and a polynomial-time algorithm for a fixed number (k) of linear graphs. Also, we strongly strengthen the result of [7] by proving that the problem is NP-complete even if ${\mathcal{G}}$ is composed of nested linear graphs of height at most 2, thereby precisely defining the borderline between tractable and intractable instances of the problem. Of particular importance, we improve the result of [7] by showing that the Max-NLS problem is approximable within ratio O(logmopt) in O(kn2) running time, where mopt is the size of an optimal solution. We also present ${{\mathcal O}}(1)$-approximation of Max-NLS problem running in ${{\mathcal O}}(kn)$ time for restricted linear graphs. In particular, for ncRNA derived linear graphs, an $\frac{1}{4}$-approximation is presented.