Related papers: Galloping in fast-growth natural merge sorts
We introduce new stable natural merge sort algorithms, called $2$-merge sort and $\alpha$-merge sort. We prove upper and lower bounds for several merge sort algorithms, including Timsort, Shivers' sort, $\alpha$-stack sorts, and our new…
Mergesort is one of the few efficient sorting algorithms and, despite being the oldest one, often still the method of choice today. In contrast to some alternative algorithms, it always runs efficiently using O(n log n) element comparisons…
Sorting is one of the oldest computing problems and is still very important in the age of big data. Various algorithms and implementation techniques have been proposed. In this study, we focus on comparison based, internal sorting…
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…
We consider the fundamental problem of internally sorting a sequence of $n$ elements. In its best theoretical setting QuickMergesort, a combination Quicksort with Mergesort with a Median-of-$\sqrt{n}$ pivot selection, requires at most $n…
The quest for efficient sorting is ongoing, and we will explore a graph-based stable sorting strategy, in particular employing comparison graphs. We use the topological sort to map the comparison graph to a linear domain, and we can…
In this paper, we present several improvements in the parallelization of the in-place merge algorithm, which merges two contiguous sorted arrays into one with an O(T) space complexity (where T is the number of threads). The approach divides…
We propose new sequential sorting operations by adapting techniques and methods used for designing parallel sorting algorithms. Although the norm is to parallelize a sequential algorithm to improve performance, we adapt a contrarian…
Recent work by Google DeepMind introduced assembly-optimized sorting networks that achieve faster performance for small fixed-size arrays (3-8). In this research, we investigate the integration of these networks as base cases in classical…
Many production-grade algorithms benefit from combining an asymptotically efficient algorithm for solving big problem instances, by splitting them into smaller ones, and an asymptotically inefficient algorithm with a very small…
This note makes an observation that significantly simplifies a number of previous parallel, two-way merge algorithms based on binary search and sequential merge in parallel. First, it is shown that the additional merge step of distinguished…
Semisort is a fundamental algorithmic primitive widely used in the design and analysis of efficient parallel algorithms. It takes input as an array of records and a function extracting a \emph{key} per record, and reorders them so that…
We present two stable mergesort variants, "peeksort" and "powersort", that exploit existing runs and find nearly-optimal merging orders with practically negligible overhead. Previous methods either require substantial effort for determining…
Merging two sorted arrays is a prominent building block for sorting and other functions. Its efficient parallelization requires balancing the load among compute cores, minimizing the extra work brought about by parallelization, and…
This paper introduces a new comparison base stable sorting algorithm, named RS sort. RS Sort involves only the comparison of pair of elements in an array which ultimately sorts the array and does not involve the comparison of each element…
We consider the problem of sorting $n$ items, given the outcomes of $m$ pre-existing comparisons. We present a simple and natural deterministic algorithm that runs in $O(m + \log T)$ time and does $O(\log T)$ comparisons, where $T$ is the…
In computer science, sorting algorithms are crucial for data processing and machine learning. Large datasets and high efficiency requirements provide challenges for comparison-based algorithms like Quicksort and Merge sort, which achieve…
Sorting is one of the fundamental problems in computer science. Playing a role in many processes, it has a lower complexity bound imposed by $\mathcal{O}(n\log{n})$ when executing on a sequential machine. This limit can be brought down to…
Various decision support systems are available that implement Data Mining and Data Warehousing techniques for diving into the sea of data for getting useful patterns of knowledge (pearls). Classification, regression, clustering, and many…
In this paper, we revisit the classic problem of run generation. Run generation is the first phase of external-memory sorting, where the objective is to scan through the data, reorder elements using a small buffer of size M , and output…