QuickXsort: Efficient Sorting with n log n - 1.399n +o(n) Comparisons on Average

In this paper we generalize the idea of QuickHeapsort leading to the notion of QuickXsort. Given some external sorting algorithm X, QuickXsort yields an internal sorting algorithm if X satisfies certain natural conditions. With QuickWeakHeapsort and QuickMergesort we present two examples for the QuickXsort-construction. Both are efficient algorithms that incur approximately n log n - 1.26n +o(n) comparisons on the average. A worst case of n log n + O(n) comparisons can be achieved without significantly affecting the average case. Furthermore, we describe an implementation of MergeInsertion for small n. Taking MergeInsertion as a base case for QuickMergesort, we establish a worst-case efficient sorting algorithm calling for n log n - 1.3999n + o(n) comparisons on average. QuickMergesort with constant size base cases shows the best performance on practical inputs: when sorting integers it is slower by only 15% to STL-Introsort

An In-Place Sorting with O(n log n) Comparisons and O(n) Moves

We present the first in-place algorithm for sorting an array of size n that performs, in the worst case, at most O(n log n) element comparisons and O(n) element transports. This solves a long-standing open problem, stated explicitly, e.g., in [J.I. Munro and V. Raman, Sorting with minimum data movement, J. Algorithms, 13, 374-93, 1992], of whether there exists a sorting algorithm that matches the asymptotic lower bounds on all computational resources simultaneously

Even faster sorting of (not only) integers

In this paper we introduce RADULS2, the fastest parallel sorter based on radix algorithm. It is optimized to process huge amounts of data making use of modern multicore CPUs. The main novelties include: extremely optimized algorithm for handling tiny arrays (up to about a hundred of records) that could appear even billions times as subproblems to handle and improved processing of larger subarrays with better use of non-temporal memory stores

Sin City?

Is moving to the countryside a credible commitment device for couples? We investigate whether lowering the arrival rate of potential alternative partners by moving to a less populated area lowers the dissolution risk for a sample of Danish couples. We find that of the couples who married in the city, the ones who stay in the city have significant higher divorce rates. Similarly, for the couples who married outside the city, the ones who move to the city are more likely to divorce. This correlation can be explained by both a causal and a sorting effect. We disentangle them by using the timing-of-events approach. In addition we use information on father’s location as an instrument. We find that the sorting effect dominates. Moving to the countryside is therefore not a cheap way to prolong relationships.dissolution; search; mobility; city

More rapid climate change promotes evolutionary rescue through selection for increased dispersal distance

Acknowledgements This research was funded by FWO projects G.0057.09 to DB and JB, and G.0610.11 to DB, JB and RS. JMJT, DB and RS are supported by the FWO Research Network EVENET.Peer reviewedPublisher PD

A Novel Hybrid Quicksort Algorithm Vectorized using AVX-512 on Intel Skylake

The modern CPU's design, which is composed of hierarchical memory and SIMD/vectorization capability, governs the potential for algorithms to be transformed into efficient implementations. The release of the AVX-512 changed things radically, and motivated us to search for an efficient sorting algorithm that can take advantage of it. In this paper, we describe the best strategy we have found, which is a novel two parts hybrid sort, based on the well-known Quicksort algorithm. The central partitioning operation is performed by a new algorithm, and small partitions/arrays are sorted using a branch-free Bitonic-based sort. This study is also an illustration of how classical algorithms can be adapted and enhanced by the AVX-512 extension. We evaluate the performance of our approach on a modern Intel Xeon Skylake and assess the different layers of our implementation by sorting/partitioning integers, double floating-point numbers, and key/value pairs of integers. Our results demonstrate that our approach is faster than two libraries of reference: the GNU \emph{C++} sort algorithm by a speedup factor of 4, and the Intel IPP library by a speedup factor of 1.4.Comment: 8 pages, research pape

Simple Symmetric Sustainable Sorting -- the greeNsort article

We explored an uncharted part of the solution space for sorting algorithms: the role of symmetry in divide&conquer algorithms. We found/designed novel simple binary Quicksort and Mergesort algorithms operating in contiguous space which achieve improved trade-offs between worst-case CPU-efficiency, best-case adaptivity and RAM-requirements. The 'greeNsort' algorithms need less hardware (RAM) and/or less energy (CPU) compared to the prior art. The new algorithms fit a theoretical framework: 'Footprint' KPIs allow to compare algorithms with different RAM-requirements, a new 'definition' of sorting API-targets simplifies construction of stable algorithms with mirrored scan directions, and our ordinal machine model encourages robust algorithms that minimize access 'distance'. Unlike earlier 'Quicksorts', our 'Zacksort', 'Zucksort' and 'Ducksort' algorithms optimally marry CPU-efficiency and tie-adaptivity. Unlike earlier 'Mergesorts' which required 100% distant buffer, our 'Frogsort' and 'Geckosort' algorithms achieve similar CPU-efficiency with 50% or less local buffer. Unlike natural Mergesorts such as 'Timsort' which are optimized for the best case of full-presorting, our 'Octosort' and 'Squidsort' algorithms achieve excellent bi-adaptivity to presorted best-cases without sacrificing worst-case efficiency in real sorting tasks. Our 'Walksort' and 'Jumpsort' have lower Footprint than the impressive low-memory 'Grailsort' and 'Sqrtsort' of Astrelin. Given the current climate-emergency, this is a call to action for all maintainers of sorting libraries, all software-engineers using custom sorting code, all professors teaching algorithms, all IT professionals designing programming languages, compilers and CPUs: check for better algorithms and consider symmetric code-mirroring.Comment: 50 pages, 6 Figures, latest version under https://github.com/greeNsort/greeNsort.article, see also https://greensort.or

Enhanced surface acoustic wave cell sorting by 3D microfluidic chip design

We demonstrate an acoustic wave driven microfluidic cell sorter that combines advantages of multilayer device fabrication with planar surface acoustic wave excitation. We harness the strong vertical component of the refracted acoustic wave to enhance cell actuation by using an asymmetric flow field to increase cell deflection. Precise control of the 3-dimensional flow is realized by topographical structures implemented on the top of the microchannel. We experimentally quantify the effect of the structure dimensions and acoustic parameter. The design attains cell sorting rates and purities approaching those of state of the art fluorescence-activated cell sorters with all the advantages of microfluidic cell sorting