Many hard examples in exact phase transitions
Theoretical Computer Science
Fourier meets möbius: fast subset convolution
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Maximum Motif Problem in Vertex-Colored Graphs
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
Limits and Applications of Group Algebras for Parameterized Problems
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Finding and counting vertex-colored subtrees
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Computing fragmentation trees from metabolite multiple mass spectrometry data
RECOMB'11 Proceedings of the 15th Annual international conference on Research in computational molecular biology
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In metabolomics and other fields dealing with small compounds, mass spectrometry is applied as sensitive high-throughput technique. Recently, fragmentation trees have been proposed to automatically analyze the fragmentation mass spectra recorded by such instruments. Computationally, this leads to the problem of finding a maximum weight subtree in an edge weighted and vertex colored graph, such that every color appears at most once in the solution. We introduce new heuristics and an exact algorithm for this Maximum Colorful Subtree problem, and evaluate them against existing algorithms on real-world datasets. Our tree completion heuristic consistently scores better than other heuristics, while the integer programming-based algorithm produces optimal trees with modest running times. Our fast and accurate heuristic can help to determine molecular formulas based on fragmentation trees. On the other hand, optimal trees from the integer linear program are useful if structure is relevant, e.g., for tree alignments.