62 research outputs found
Worst-Case Efficient Sorting with QuickMergesort
The two most prominent solutions for the sorting problem are Quicksort and
Mergesort. While Quicksort is very fast on average, Mergesort additionally
gives worst-case guarantees, but needs extra space for a linear number of
elements. Worst-case efficient in-place sorting, however, remains a challenge:
the standard solution, Heapsort, suffers from a bad cache behavior and is also
not overly fast for in-cache instances.
In this work we present median-of-medians QuickMergesort (MoMQuickMergesort),
a new variant of QuickMergesort, which combines Quicksort with Mergesort
allowing the latter to be implemented in place. Our new variant applies the
median-of-medians algorithm for selecting pivots in order to circumvent the
quadratic worst case. Indeed, we show that it uses at most
comparisons for large enough.
We experimentally confirm the theoretical estimates and show that the new
algorithm outperforms Heapsort by far and is only around 10% slower than
Introsort (std::sort implementation of stdlibc++), which has a rather poor
guarantee for the worst case. We also simulate the worst case, which is only
around 10% slower than the average case. In particular, the new algorithm is a
natural candidate to replace Heapsort as a worst-case stopper in Introsort
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