Physical map assembly is the inference of genome structure from experimental data. Map assembly depends on the integration of diverse data including sequence tagged site (STS) marker content, clone sizing, and restriction digest fingerprints (RDF). As experimentally measured data, these are uncertain and error prone. Physical map assembly from error free data is straightforward and can be accomplished in linear time in the number of clones, but the assembly of an optimal map from error prone data is an NP-hard problem. We present an alternative approach to physical map assembly that is based on a probabilistic view of the data and seeks to identify those features of the map that can be reliably inferred from the available data. With this approach, we achieve a number of goals. These include the use of multiple data sources, appropriate representation of uncertainties in the underlying data, the use of clone length information in fingerprint map assembly, and the use of higher order information in map assembly. By higher order information, we mean relationships that are not expressible in terms of neighbouring clone relationships. These include triplet and multiple clone overlaps, the uniqueness of STS position, and fingerprint marker locations. In a probabilistic view of physical mapping, we assert that all of the many possible map assemblies are equally likely a priori. Given experimental data, we can only state which assemblies are more likely than others given the experimental observations. Parameters of interest are then derived as likelihood weighted averages over map assemblies. Ideally these averages should be sums or integrals over all possible map assemblies, but computationally this is not feasible for real-world map assembly problems. Instead, sampling is used to asymptotically approach the desired parameters. Software implementing our probabilistic approach to mapping has been written. Assembly of mixed RDF and STS maps containing up to 60 clones can be accomplished on a desktop PC with run times under an hour.