Abstract: In this paper, we describe our algorithmic approach to constructing an alignment (Contig) of a set of optical maps created from the images of individual genomic DNA molecules digested by restriction enzymes. Generally, these DNA segments are sized in the range of 1--4 Mb. The problem of assembling clone contig maps is a simpler special case of this contig problem and is handled by our algorithms. 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 routinely to create composite maps of various microorganisms (E.coli, P.falciparum and D.radioduran). The experimental results appear highly promising.