Fragmentation trees are a technique for identifying molecular formulas and deriving some chemical properties of metabolitessmall organic moleculessolely from mass spectral data. Computing these trees involves nding exact solutions to the NP-hard Maximum Colorful Subtree problem. Existing solvers struggle to solve the large instances involved fast enough to keep up with instrument throughput, and their performance remains a hindrance to adoption in practice. We attack this problem on two fronts:

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... by combining fast and eective reduction algorithms with a strong integer linear program (ILP) formulation of the problem, we achieve overall speedups of 9.4 fold and 8.8 fold on two sets of real-world problemswithout sacricing optimality. Both approaches are, to our knowledge, the rst of their kind for this problem. We also evaluate the strategy of solving global problem instances, instead of rst subdividing them into many candidate instances as has been done in the past. Software (C++ source for our reduction program and our CPLEX/Gurobi driver program) available under LGPL at https://github.com/wtwhite/ speedy_colorful_subtrees/.