Timsort, the Python sorting algorithm
You can beat O(n log n). That limit is for sorts that use only a ">" comparison. A distribution sort, where you distribute the keys over buckets, can approach O(n).The first software patent, for SyncSort, is for a sort that beats O(n log n). The basic idea is to read records for a while, get some stats about the key distribution, and set up the buckets to get a roughly equal fraction of the observed keyspace.  If blocks of records show up with very different stats, action has to be taken to adjust the bucketing.