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Abstract: We present a new data structure called the \emph{Compressed Random AccessMemory} CRAM that can store a dynamic string $T$ of characters, e.g.,representing the memory of a computer, in compressed form while achievingasymptotically almost-optimal bounds in terms of empirical entropy on thecompression ratio. It allows short substrings of $T$ to be decompressed andretrieved efficiently and, significantly, characters at arbitrary positions of$T$ to be modified quickly during execution \emph{without decompressing theentire string}. This can be regarded as a new type of data compression that canupdate a compressed file directly. Moreover, at the cost of slightly increasingthe time spent per operation, the CRAM can be extended to also supportinsertions and deletions. Our key observation that the empirical entropy of astring does not change much after a small change to the string, as well as oursimple yet efficient method for maintaining an array of variable-length blocksunder length modifications, may be useful for many other applications as well.



Author: Jesper Jansson, Kunihiko Sadakane, Wing-Kin Sung

Source: https://arxiv.org/







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