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In this work we define a novel metric structure to work with functions defined on merge trees. The metric introduced possesses some stability properties and can be computed with a dynamical integer linear programming approach. We showcase its feasibility and the effectiveness of the whole framework with simulated data sets. Using functions defined on merge trees proves to be very effective in situation where other topological data analysis tools, like persistence diagrams, can not be meaningfully employed.arXiv:2108.13108v6 fatcat:jmtv23doofa7fpol62q4emo6fq