Partitioning single-molecule maps into multiple populations: Algorithms and probabilistic analysis

Given a set of m molecules, derived from K homologous clones, we wish to partition these molecules into K populations, each giving rise to distinct ordered restriction maps, thus providing simple means for studying biological variations. With the emergence of single-molecule methods, such as optical mapping, that can create individual ordered restriction maps reliably and with high throughput, it becomes interesting to study the related algorithmic problems. In particular, we provide a complete computational complexity analysis of the "K-populations" problem along with a probabilistic analysis. We also present some simple polynomial heuristics, while exposing the relations among various error sources that the optical mapping approach may need to cope with. We believe that these results will be of interest to computational biologists in devising better algorithms, to biochemists in understanding the trade-offs among the error sources and finally, to biologists in creating reliable protocols for population study.