An efficient transitive closure algorithm for cyclic digraphs
Information Processing Letters
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
Note: Computational complexity of some restricted instances of 3-SAT
Discrete Applied Mathematics
Fourier meets möbius: fast subset convolution
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Complexity issues in vertex-colored graph pattern matching
Journal of Discrete Algorithms
Sharp tractability borderlines for finding connected motifs in vertex-colored graphs
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Finding maximum colorful subtrees in practice
RECOMB'12 Proceedings of the 16th Annual international conference on Research in Computational Molecular Biology
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Since metabolites cannot be predicted from the genome sequence, high-throughput de-novo identification of small molecules is highly sought. Mass spectrometry (MS) in combination with a fragmentation technique is commonly used for this task. Unfortunately, automated analysis of such data is in its infancy. Recently, fragmentation trees have been proposed as an analysis tool for such data. Additional fragmentation steps (MSn) reveal more information about the molecule. We propose to use MSn data for the computation of fragmentation trees, and present the COLORFUL SUBTREE CLOSURE problem to formalize this task: There, we search for a colorful subtree inside a vertexcolored graph, such that the weight of the transitive closure of the subtree is maximal. We give several negative results regarding the tractability and approximability of this and related problems. We then present an exact dynamic programming algorithm, which is parameterized by the number of colors in the graph and is swift in practice. Evaluation of our method on a dataset of 45 reference compounds showed that the quality of constructed fragmentation trees is improved by using MSn instead of MS2 measurements.