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Background  During cancer progression genomes undergo point mutations as well as larger segmental changes. The latter include, among others, segmental deletions duplications, translocations and inversions.The result is a highly complex, patient-specific cancer karyotype. Using high-throughput technologies of deep sequencing and microarrays it is possible to interrogate a cancer genome and produce chromosomal copy number profiles and a list of breakpoints (“jumps”) relative to the normal genome. This information is very detailed but local, and does not give the overall picture of the cancer genome. One of the basic challenges in cancer genome research is to use such information to infer the cancer karyotype.  We present here an algorithmic approach, based on graph theory and integer linear programming, that receives segmental copy number and breakpoint data as input and produces a cancer karyotype that is most concordant with them. We used simulations to evaluate the utility of our approach, and applied it to real data.    Results  By using a simulation model, we were able to estimate the correctness and robustness of the algorithm in a spectrum of scenarios. Under our base scenario, designed according to observations in real data, the algorithm correctly inferred 69% of the karyotypes. However, when using less stringent correctness metrics that account for incomplete and noisy data, 87% of the reconstructed karyotypes were correct. Furthermore, in scenarios where the data were very clean and complete, accuracy rose to 90%–100%. Some examples of analysis of real data, and the reconstructed karyotypes suggested by our algorithm, are also presented.    Conclusion  While reconstruction of complete, perfect karyotype based on short read data is very hard, a large fraction of the reconstruction will still be correct and can provide useful information.    Electronic supplementary material  The online version of this article (10.1186/s12859-017-1929-9) contains supplementary material, which is available to authorized users.

Reconstructing cancer karyotypes from short read data: the half empty and half full glass