Organic Mergesort and Finger Buffer-Tree Sort: Adaptive Sorting Algorithms with External-Memory or Parallel Implementations

We describe two adaptive sorting paradigms, organic mergesort and finger buffer-tree sort, which have parallel or external-memory implementations. Depending on the implementation regime, our mergesort algorithms have optimal time, work, and/or input/output (I/O) operations with respect to the run-based entropy of the input sequence, which matches the performance of optimal sequential internal-memory natural mergesort algorithms, such as Timsort, Peeksort, and Powersort.