A generic genotyping assay utilizes a fixed set of reagents, which is independent of the actual target sample, to determine all present alleles. An example is the interrogation of several amplicons spanning polymorphic sites using an all k-mer array. Due to the high cost associated with a genotyping experiment, it is desirable to design a set of experiments, which maximizes the number of SNPs that can be genotyped in parallel per assay. In this study we investigate algorithmic approaches for optimally multiplexing SNP genotyping using generic assays. We devise a graph theoretic formulation of the problem and use it to derive an approximation algorithm for the problem, and several practical heuristics. We apply our methods to simulated and real data, for evaluating the multiplexing rates afforded by generic techniques. The results on real human data show the practicality of generic approaches for genotyping, allowing, e.g., the genotyping of 5000 SNPs using four all 7-mer arrays.