Abstract: A system partitions files, including segments identified by fingerprints. into clusters. The system counts common fingerprints by counting fingerprints which correspond to both a file cluster and another file cluster. The system counts unique fingerprints by counting fingerprints which correspond to the file cluster and/or the other file cluster. The system uses the common and unique fingerprint counts to approximate the distance between the file cluster and the other file cluster. The system identifies the smallest of distances which are approximated between all file clusters. The system merges the file cluster and the other file cluster into a merged file cluster if the approximated distance is the smallest of distances. The system determines an index corresponding to the smallest and next smallest of distances. The system determines indexes which correspond to merges of all file clusters. The system uses the maximum of indexes to identify the optimal file clustering.

Abstract: Identify first file's minimum value from at least value from applying function to first file's segment and value from applying function to first file's second segment. Identify first file's second minimum value from at least value from applying second function to first file's segment and value from applying second function to first file's second segment. Identify second file's minimum value from at least value from applying function to second file's segment and value from applying function to second file's second segment. Identify second file's second minimum value from at least value from applying second function to second file's segment and value from applying second function to second file's second segment. Estimate first and second files' union size based on whether first file's minimum value equals second file's minimum value, whether first file's second minimum value equals second file's second minimum value, first file's size, and second file's size.

Abstract: A system partitions files, including segments identified by fingerprints. into clusters. The system counts common fingerprints by counting fingerprints which correspond to both a file cluster and another file cluster. The system counts unique fingerprints by counting fingerprints which correspond to the file cluster and/or the other file cluster. The system uses the common and unique fingerprint counts to approximate the distance between the file cluster and the other file cluster. The system identifies the smallest of distances which are approximated between all file clusters. The system merges the file cluster and the other file cluster into a merged file cluster if the approximated distance is the smallest of distances. The system determines an index corresponding to the smallest and next smallest of distances. The system determines indexes which correspond to merges of all file clusters. The system uses the maximum of indexes to identify the optimal file clustering.