Compressed Transitive Delta Encoding

Given a source file $S$ and two differencing files $\Delta (S,T)$ and $\Delta(T,R)$, where $\Delta(X,Y)$ is used to denote the delta file of the target file $Y$ with respect to the source file $X$, the objective is to be able to construct $R$.This is intended for the scenario of upgrading software where intermediate releases are missing, or for the case of file system backups, where non consecutive versions must be recovered.The traditional way is to decompress $\Delta(S,T)$ in order to construct$T$ and then apply $\Delta(T,R)$ on $T$ and obtain $R$.The {\it Compressed Transitive Delta Encoding (CTDE)} paradigm, introduced in this paper, is to  construct a delta file $\Delta(S,R)$ working directly on the two given delta files, $\Delta (S,T)$ and $\Delta(T,R)$, without any decompression or the use of the base file $S$. A new algorithm for solving CTDE is proposed and its compression performance is compared against the traditional ``double delta decompression''.Not only does it use constant additional space, as opposed to  the traditional method which uses linear additional memory storage, but experiments show that the size of the delta files involved is reduced by 15\% on average.