A Uniform Framework for Ordered Restriction Map Problems

Optical Mapping is an emerging technology for constructing ordered restriction maps of DNA molecules. The underlying computational problems for this technology have been studied and several models have been proposed in recent literature. Most of these propose combinatorial models; some of them also present statistical approaches. However, it is not a priori clear as to how these models relate to one another and to the underlying problem. We present a uniform framework for the restriction map problems where each of these various models is a specific instance of the basic framework. We achieve this by identifying two "signature" functions f() and g() that characterize the models. We identify the constraints these two functions must satisfy, thus opening up the possibility of exploring other plausible models. We show that for all of the combinatorial models proposed in literature, the signature functions are semi-algebraic. We also analyze a proposed statistical method in this framework and show that the signature functions are transcendental for this model. We also believe that this framework would provide useful guidelines for dealing with other inferencing problems arising in practice. Finally, we indicate the open problems by including a survey of the best known results for these problems.