Abstract Many cancer genomes are extensively rearranged with highly aberrant chromosomal karyotypes. These genome rearrangements, or structural variants, can be detected in tumor DNA sequencing data by abnormal mapping of se-quence reads to the reference genome. However, nearly all cancer sequencing to date is of bulk tumor samples which consist of a heterogeneous mixture of normal cells and subpopulations of cancers cells, or clones, that harbor distinct somatic structural variants. We introduce a novel algorithm, R econstructing C ancer K aryotypes ( RCK ), to reconstruct haplotype-specific karyotypes of one or more rearranged cancer genomes, or clones, that best explain the read alignments from a bulk tumor sample. RCK leverages specific evolutionary constraints on the somatic mutation process in cancer to reduce ambiguity in the deconvolution of admixed DNA sequence data into multiple haplotype-specific cancer karyotypes. In particular, RCK relies on generalizations of the infinite sites assumption that a genome re-arrangement is highly unlikely to occur at the same nucleotide position more than once during somatic evolution. RCK ’s comprehensive model allows us to incorporate information both from short and long-read sequencing technologies and is applicable to bulk tumor samples containing a mixture of an arbitrary number of derived genomes. We compared RCK to the state-of-the-art method ReMixT on a dataset of 17 primary and metastatic prostate cancer samples. We demonstrate that ReMixT ’s limited support for heterogeneity and lack of evolutionary constrains leads to reconstruction of implausible karyotypes. In contrast, RCK ’s infers cancer karyotypes that better explain read alignments from bulk tumor samples and are consistent with a reasonable evolutionary model. RCK ’s reconstructions of clone- and haplotype-specific karyotypes will aid further studies of the role of intra-tumor heterogeneity in cancer development and response to treatment. RCK is available at https://github.com/raphael-group/RCK .

Reconstruction of clone- and haplotype-specific cancer genome karyotypes from bulk tumor samples