Related papers: Emerge-Sort: Converging to Ordered Sequences by Si…
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…
Sorting algorithms are fundamental to computer science, and their correctness criteria are well understood as rearranging elements of a list according to a specified total order on the underlying set of elements. As mathematical functions,…
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…
We introduce a sorting machine consisting of $k+1$ stacks in series: the first $k$ stacks can only contain elements in decreasing order from top to bottom, while the last one has the opposite restriction. This device generalizes \cite{SM},…
The dynamic partial sorting problem asks for an algorithm that maintains lists of numbers under the link, cut and change value operations, and queries the sorted sequence of the $k$ least numbers in one of the lists. We first solve the…
We present the first explicit comparison-based algorithm that sorts the sumset $X + Y = \{x_i + y_j,\ \forall 0 \le i, j < n\}$, where $X$ and $Y$ are sorted arrays of real numbers, in optimal $O(n^2)$ time and comparisons. While Fredman…
In sorting situations where the final destination of each item is known, it is natural to repeatedly choose items and place them where they belong, allowing the intervening items to shift by one to make room. (In fact, a special case of…
The original Leapfrogging Samplesort operates on a sorted sample of size $s$ and an unsorted part of size $s+1$. We generalize this to a sorted sample of size $s$ and an unsorted part of size $(2^k-1)(s+1)$, where $k = O(1)$. We present a…
Unconditional scene inference and generation are challenging to learn jointly with a single compositional model. Despite encouraging progress on models that extract object-centric representations (''slots'') from images, unconditional…
LearnedSort is a novel sorting algorithm that, unlike traditional methods, uses fast ML models to boost the sorting speed. The models learn to estimate the input's distribution and arrange the keys in sorted order by predicting their…
Recurrence equations have played a central role in static cost analysis, where they can be viewed as abstractions of programs and used to infer resource usage information without actually running the programs with concrete data. Such…
In this paper, we introduce and prove QR Sort, a novel non-comparative integer sorting algorithm. This algorithm uses principles derived from the Quotient-Remainder Theorem and Counting Sort subroutines to sort input sequences stably. QR…
Arranging objects correctly is a key capability for robots which unlocks a wide range of useful tasks. A prerequisite for creating successful arrangements is the ability to evaluate the desirability of a given arrangement. Our method…
We study the problem of sorting under incomplete information, when queries are used to resolve uncertainties. Each of $n$ data items has an unknown value, which is known to lie in a given interval. We can pay a query cost to learn the…
We study the impact of merging routines in merge-based sorting algorithms. More precisely, we focus on the galloping routine that TimSort uses to merge monotonic sub-arrays, hereafter called runs, and on the impact on the number of element…
Event Shape Sorting is a novel method which is devised to organise a sample of collision events in such a way, that events with similar final state distribution of hadrons end up sorted close to each other. Such events are likely to have…
In this paper we study the problem of sorting under non-uniform comparison costs, where costs are either 1 or $\infty$. If comparing a pair has an associated cost of $\infty$ then we say that such a pair cannot be compared (forbidden…
The exponential ordering is exploited in the context of non-auto\-no\-mous delay systems, inducing monotone skew-product semiflows under less restrictive conditions than usual. Some dynamical concepts linked to the order, such as…
We engineer algorithms for sorting huge data sets on massively parallel machines. The algorithms are based on the multiway merging paradigm. We first outline an algorithm whose I/O requirement is close to a lower bound. Thus, in contrast to…
Emergence in machine learning refers to the spontaneous appearance of complex behaviors or capabilities that arise from the scale and structure of training data and model architectures, despite not being explicitly programmed. We introduce…