Abstract: Nucleic acid sequence mapping/assembly methods are disclosed. The methods initially map only a contiguous portion of each read to a reference sequence and then extends the mapping of the read at both ends of the mapped contiguous portion until the entire read is mapped (aligned). In various embodiments, a mapping score can be calculated for the read alignment using a scoring function, score (i, j)=M+mx, where M can be the number of matches in the extended alignment, x can be the number of mismatches in the alignment, and m can be a negative penalty for each mismatch. The mapping score can be utilized to rank or choose the best alignment for each read.