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Abstract Motivation In recent years, the well-known Infinite Sites Assumption (ISA) has been a fundamental feature of computational methods devised for reconstructing tumor phylogenies and inferring cancer progressions. However, recent studies leveraging Single-Cell Sequencing (SCS) techniques have shown evidence of the widespread recurrence and, especially, loss of mutations in several tumor samples. While there exist established computational methods that infer phylogenies with mutation losses, there remain some advancements to be made. Results We present SASC (Simulated Annealing Single-Cell inference): a new and robust approach based on simulated annealing for the inference of cancer progression from SCS data sets. In particular, we introduce an extension of the model of evolution where mutations are only accumulated, by allowing also a limited amount of mutation loss in the evolutionary history of the tumor: the Dollo-k model. We demonstrate that SASC achieves high levels of accuracy when tested on both simulated and real data sets and in comparison with some other available methods. Availability The Simulated Annealing Single-Cell inference (SASC) tool is open source and available at https://github.com/sciccolella/sasc. Supplementary information Supplementary data are available at Bioinformatics online.