Abstract
Recently, Hajirasouliha and Raphael (WABI 2014) proposed a model for deconvoluting mixed tumor samples measured from a collection of high-throughput sequencing reads. This is related to understanding tumor evolution and critical cancer mutations. In short, their formulation asks to split each row of a binary matrix so that the resulting matrix corresponds to a perfect phylogeny and has the minimum number of rows among all matrices with this property. In this paper we disprove several claims about this problem, including an NP-hardness proof of it. However, we show that the problem is indeed NP-hard, by providing a different proof. We also prove NP-completeness of a variant of this problem proposed in the same paper. On the positive side, we obtain a polynomial time algorithm for matrix instances in which no column is contained in both columns of a pair of conflicting columns.
This work was supported in part by the Slovenian Research Agency (I0-0035, research program P1-0285, research projects N1-0032, J1-5433, J1-6720, and J1-6743), by the bilateral project BI-FR/15–16–PROTEUS–003, and by the Academy of Finland, grant 274977.
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Hujdurović, A., Kačar, U., Milanič, M., Ries, B., Tomescu, A.I. (2015). Finding a Perfect Phylogeny from Mixed Tumor Samples. In: Pop, M., Touzet, H. (eds) Algorithms in Bioinformatics. WABI 2015. Lecture Notes in Computer Science(), vol 9289. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48221-6_6
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DOI: https://doi.org/10.1007/978-3-662-48221-6_6
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