Using difficulty of prediction to decrease computation: fast sort, priority queue and convex hull on entropy bounded inputs

Studies have indicated that sorting comprises about 20% of all computing on mainframes. Perhaps the largest use of sorting in computing (particularly business computing) is the sort required for large database operations (e.g. required by joint operations). In these applications the keys are many words long. Since our sorting algorithm hashes the key (rather than compare entire keys as in comparison sorts such as quicksort), our algorithm is even more advantageous in the case of large key lengths; in that case the cutoff is much lower. In case that the compression ratio is high, which can be determined after building the dictionary, we just adopt the previous sorting algorithm, e.g. quick sort. The same techniques can be extended to other problems (e.g. computational geometry problems) to decrease computation by learning the distribution of the inputs