This thesis is motivated by the latest work related to differential compression algorithms as it appears in the work of Ajtai, et al. - 2002. In particular, we pay special attention to delta encoding algorithms that achieve got compression in linear time and constant space. This is important because previous work in this area uses either quadratic time and constant space or linear time and linear space, which is unacceptable for large inputs. In delta encoding, the algorithm reads two different copies of the same file as input, termed the reference copy and the version copy. The output of the ...