Reducing Fragmentation in Data Deduplication Systems via Partial Repetition and Coding

Data deduplication, one of the key features of modern Big Data storage devices, is the process of removing replicas of data chunks stored by different users. Despite the importance of deduplication, several drawbacks of the method, such as storage robustness and file fragmentation, have not been previously analyzed from a theoretical point of view. Storage robustness pertains to ensuring that deduplicated data can be used to reconstruct the original files without service disruptions and data loss. Fragmentation pertains to the problems of placing deduplicated data chunks of different user files in a proximity-preserving linear order, since neighboring chunks of the same file may be stored in sectors far apart on the server. This work proposes a new theoretical model for data fragmentation and introduces novel graph- and coding-theoretic approaches for reducing fragmentation via limited duplication (repetition coding) and coded deduplication (e.g., linear coding). In addition to alleviating issues with fragmentation, limited duplication and coded deduplication can also serve the dual purpose of increasing the robusteness of the system design. The contributions of our work are three-fold. First, we describe a new model for file structures of the form of self-avoiding (simple) paths in specialized graphs. Second, we introduce several new metrics for measuring the fragmentation level in deduplication systems on graph-structured files, including the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">stretch metric</i> that captures the worst-case “spread” of adjacent data chunks within a file when deduplicated and placed on the server; and, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">jump metric</i> that captures the worst-case number of times during the reconstruction process of a file that one has to change the readout location on the server. For the stretch metric, we establish a connection between the level of fragmentation and the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">bandwidth</i> of the file-graph. In particular, we derive lower and upper bounds on the degree of fragmentation and describe instances of the problem where repetition and coding reduce fragmentation. The key ideas behind our approach are graph folding and information-theoretic arguments coupled with graph algorithms such as matching. For the jump metric, we provide a new algorithm for computing the jump number of hierarchical data structures captured by trees. Third, we describe how controlled repetition and coded redundancy added after deduplication can ensure valuable trade-offs between the storage volume and the degree of fragmentation.