Overview of the RCK algorithm. The inputs to RCK (white dotted boxes) are clone- and allele-specific copy numbers (top left) and novel adjacencies (top right) from bulk tumor samples that are derived from alignments of DNA sequencing (top) reads using existing tools. The RCK algorithm (blue shaded elements) builds a diploid interval adjacency graph integrating copy number and novel adjacency information (for details, see Methods). RCK then solves a mixed-integer linear program (MILP) to find an optimal assignment of segment copy numbers and novel adjacencies to alleles and clones, subject to copy number balance on segment ends and satisfying evolutionary constraints from a generalized infinite sites model. Constraints on groups of novel adjacencies from the third-generation sequencing technologies may optionally be included. The outputs of RCK are clone- and haplotype-specific cancer genome karyotypes.