Bipartite graphs are widely used for modeling of complex structures in biology, engineering, and computer science. The search for shortest paths in such structures is a highly demanded procedure that requires optimization. This paper presents a variant of the all-pairs shortest path algorithm for bipartite graphs. The method is based on the distance matrix product and improves the general algorithm by exploiting the graph topology. The space complexity is reduced by a factor of at least four and the time complexity decreased by almost an order of magnitude when compared with the basic APSP algorithm.
A careful design of DNA strands is crucial for several biological applications such as microarray techniques, Polymerase Chain Reaction (PCR), and DNA computing. For this, the important criterion under laboratory conditions is the hybridisation energy of two DNA strands. During the last decade, a thermodynamic model was developed that allows for the calculation of the DNA/DNA hybridisation energy and recently also the cross-hybridisation energy of structural motifs. Employing this model a new algorithm for the secondary structure prediction of DNA/DNA cross-hybridisation complexes called HYBGRAPH is introduced. The method is based on Gibbs free energy minimisation and the paradigm of dynamic programming.
Alignment is one of the basic operations in molecular biology to compare sequences. The most widely used methods for multiple sequence alignment include scalar-product based alignment of groups of sequences. We show that scalar-product based alignment algorithms can be significantly speeded up by generalpurpose computing on a modern commonly available graphics card. Thus the huge computational power of graphics cards can be exploited to develop high performance solutions for multiple sequence alignment.
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