Fragmentation in Data Deduplication Systems II: The Jump Metric

Data deduplication refers to a collection of data processing strategies that aim to remove repeated data chunks stored by different users. Despite providing excellent storage savings, deduplication can lead to severe file fragmentation issues: data chunks of the same file may be stored at distal locations on the server, making reconstruction time-consuming. Here, we continue our analytical study of uncoded and coded deduplication methods with reduced fragmentation levels. We model files as self-avoiding (simple) paths in specialized graphs whose nodes correspond to data chunks. To measure the level of fragmentation, we introduce the jump metric which 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. We derive lower and upper bounds on the degree of jump fragmentation, and provide a new algorithm for computing the jump number of hierarchical data structures captured by trees. We also present examples that show how repetition and coded redundancy in chunk stores can reduce jump fragmentation.