Rectifying corrupted files in distributed file systems

A probabilistic comparison algorithm is presented which requires O(f log n) bits to be transmitted to identify the corrupt pages in a file (where n is the number of pages and f is the maximum number of pages that could be corrupted), which improves on previous results on the growth of communicated bits as functions of both n and of f. If both copies compared are corrupt, only twice the number of bits is required as for the previous case. Further, if multiple copies are used for comparison, then the product of the number of copies times the number of bits sent from each of these copies to the comparison site grows as O(f log n). A lower bound which establishes the optimality of the algorithm to within a constant factor is provided