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Abstract Background Cancer progression reconstruction is an important development stemming from the phylogenetics field. In this context, the reconstruction of the phylogeny representing the evolutionary history presents some peculiar aspects that depend on the technology used to obtain the data to analyze: Single Cell DNA Sequencing data have great specificity, but are affected by moderate false negative and missing value rates. Moreover, there has been some recent evidence of back mutations in cancer: this phenomenon is currently widely ignored. Results We present a new tool, , that reconstructs a tumor phylogeny from Single Cell Sequencing data, allowing each mutation to be lost at most a fixed number of times. The General Parsimony Phylogeny from Single cell () tool is open source and available at https://github.com/AlgoLab/gpps . Conclusions provides new insights to the analysis of intra-tumor heterogeneity by proposing a new progression model to the field of cancer phylogeny reconstruction on Single Cell data.