Multiway Powersort

Powersort (Munro & Wild, ESA2018) has recently replaced Timsort's suboptimal merge policy in the CPython reference implementation of Python, as well as in PyPy and further libraries. We present a stable mergesort variant, Multiway Powersort, that exploits existing runs and finds nearly-optimal merging orders for k-way merges with negligible overhead. As observed with Multiway Quicksort (Kushagra et al., ALENEX 2014; Aum\"uller & Dietzfelbinger, TALG 2016; Wild, PhD thesis 2016) and the inclusion of Dual-Pivot Quicksort in the Java runtime library, memory transfers increasingly determine the cost of internal sorting. We demonstrate that our 4-way Powersort implementation can achieve substantial speedups over standard (2-way) Powersort and other stable sorting methods without compromising the optimally run-adaptive performance of Powersort.