DNA sequences are cut into smaller fragments using restriction enzymes in order to facilitate analysis. Application of different restriction enzymes to multiple copies of a DNA sequence generates many overlapping fragments. To reconstruct the original DNA, these fragments need to be sequenced and assembled. This problem of finding the original order of the fragments is called the genome map assembly problem. We propose a constraint automaton solution to solve the genome map assembly problem for both error prone and error free data. Plasmid vectors puc57, pKLAC1-malE, pTXB1 and phage vector Adenovirus2, having a size in base pairs of 2710, 6706, 10153 and 35937 respectively, were used to prove that computational time for solving genome map assembly problem using constraint automaton solution is linear with both precise and approximate data.