Population low-coverage whole-genome sequencing is rapidly emerging as a prominent approach for discovering genomic variation and genotyping a cohort. This approach combines substantially lower cost than full-coverage sequencing with whole-genome discovery of low-allele frequency variants, to an extent that is not possible with array genotyping or exome sequencing. However, a challenging computational problem arises of jointly discovering variants and genotyping the entire cohort. Variant discovery and genotyping are relatively straightforward tasks on a single individual that has been sequenced at high coverage, because the inference decomposes into the independent genotyping of each genomic position for which a sufficient number of confidently mapped reads are available. However, in low-coverage population sequencing, the joint inference requires leveraging the complex linkage disequilibrium (LD) patterns in the cohort to compensate for sparse and missing data in each individual. The potentially massive computation time for such inference, as well as the missing data that confound low-frequency allele discovery, need to be overcome for this approach to become practical.