The key building blocks for cloud computing applications are Distributed File Systems which are based on the Map Reduce programming paradigm. Nodes simultaneously serve computing and storage functions In such file systems. A file is partitioned into a number of chunks allocated in distinct nodes in order so, over the nodes, MapReduce tasks can be performed in parallel. However, failure is the norm in a cloud computing environment. In the system, nodes may be either upgraded, or replaced, or added. Files can also be dynamically created, or deleted, and appended. Our algorithm is compared against a centralized approach in a production system and a competing distributed solution presented in the literature. The results indicate that our proposal is comparable with the existing centralized approach. It also considerably outperforms the prior distributed algorithm in terms of load imbalance factor, movement cost, and algorithmic overhead.