Min cut is NP-complete for edge weighted trees
Theoretical Computer Science - Thirteenth International Colloquim on Automata, Languages and Programming, Renne
Graphs with small bandwidth and cutwidth
Discrete Mathematics
Crossing Minimization in Linear Embeddings of Graphs
IEEE Transactions on Computers
Tree-width, path-width, and cutwidth
Discrete Applied Mathematics
Dynamic programming algorithms for RNA secondary structure prediction with pseudoknots
Discrete Applied Mathematics - Special volume on combinatorial molecular biology
BIBE '01 Proceedings of the 2nd IEEE International Symposium on Bioinformatics and Bioengineering
Cutwidth I: a linear time fixed parameter algorithm
Journal of Algorithms
Cutwidth II: algorithms for partial w-trees of bounded degree
Journal of Algorithms
Parameterized Complexity
On cutwidth parameterized by vertex cover
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Variable Formulation Search for the Cutwidth Minimization Problem
Applied Soft Computing
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In the context of protein engineering, we consider the problem of computing an mRNA sequence of maximal codon-wise similarity to a given mRNA (and consequently, to a given protein) that additionally satisfies some secondary structure constraints, the so-called mRNA Structure Optimization (MRSO) problem. Since MRSO is known to be APX-hard, Bongartz [D. Bongartz, Some notes on the complexity of protein similarity search under mRNA structure constraints, in: Proc. of the 30th Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM), 2004, pp. 174-183] suggested to attack the problem using the approach of parameterized complexity. In this paper we propose three fixed-parameter algorithms that apply for several interesting parameters of MRSO. We believe these algorithms to be relevant for practical applications today, as well as for possible future applications. Furthermore, our results extend the known tractability borderline of MRSO, and provide new research horizons for further improvements of this sort.