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Herein, we report a computational algorithm that follows a spectroscopist-driven elucidation process of the structure of an organic molecule based on IR, 1H and 13C NMR, and MS tabular data. The algorithm is independent from database searching and is based on a bottom-up approach, building the molecular structure from small structural fragments visible in spectra. It employs an analytical combinatorial approach with a graph search technique to determine the connectivity of structural fragments that is based on the analysis of the NMR spectra, to connect the identified structural fragments into a molecular structure. After the process is completed, the interface lists the compound candidates, which are visualized by the WolframAlpha computational knowledge engine within the interface. The candidates are ranked according to the predefined rules for analyzing the spectral data. The developed elucidator has a user-friendly web interface and is publicly available (http://schmarnica.si).