In this paper, we describe our algorithmic approach to constructing an alignment of (contiging) a set of restriction maps created from the images of individual genomic (uncloned) DNA molecules digested by restriction enzymes. Generally, these DNA segments are sized in the range of 1-4Mb. The goal is to devise contiging algorithms capable of producing high-quality composite maps rapidly and in a scalable manner. The resulting software is a key component of our physical mapping automation tools and has been used to create complete maps of various microorganisms (E. coli, P. falciparum and D. radiodurans). Experimental results match known sequence data.