  In metabolomics, small molecules are structurally elucidated using tandem
mass spectrometry (MS/MS); this resulted in the computational Maximum Colorful
Subtree problem, which is NP-hard. Unfortunately, data from a single metabolite
requires us to solve hundreds or thousands of instances of this problem; and in
a single Liquid Chromatography MS/MS run, hundreds or thousands of metabolites
are measured.
  Here, we comprehensively evaluate the performance of several heuristic
algorithms for the problem against an exact algorithm. We put particular
emphasis on whether a heuristic is able to rank candidates such that the
correct solution is ranked highly. We propose this "intermediate" evaluation
because evaluating the approximating quality of heuristics is misleading: Even
a slightly suboptimal solution can be structurally very different from the true
solution. On the other hand, we cannot structurally evaluate against the ground
truth, as this is unknown. We find that one particular heuristic consistently
ranks the correct solution in a top position, allowing us to speed up
computations about 100-fold. We also find that scores of the best heuristic
solutions are very close to the optimal score; in contrast, the structure of
the solutions can deviate significantly from the optimal structures.
