Related papers: Intrinsically Correct Sorting in Cubical Agda
We introduce order conserving embeddings as a more general form of order preserving embeddings between finite dimensional nest algebras. The structure of these embeddings is determined, in terms of order indecomposable decompositions, and…
A novel integer value-sorting technique is proposed replacing bucket sort, distribution counting sort and address calculation sort family of algorithms. It requires only constant amount of additional memory. The technique is inspired from…
Biclustering, also known as co-clustering or two-way clustering, simultaneously partitions the rows and columns of a data matrix to reveal submatrices with coherent patterns. Incorporating background knowledge into clustering to enhance…
We introduce Voevodsky's univalent foundations and univalent mathematics, and explain how to develop them with the computer system Agda, which is based on Martin-L\"of type theory. Agda allows us to write mathematical definitions,…
Studying the set of exact solutions of a system of polynomial equations largely depends on a single iterative algorithm, known as Buchberger's algorithm. Optimized versions of this algorithm are crucial for many computer algebra systems…
In the algorithm Intersort, Chevalley et al. (2024) proposed a score-based method to discover the causal order of variables in a Directed Acyclic Graph (DAG) model, leveraging interventional data to outperform existing methods. However, as…
Cylindrical algebraic decompositions (CADs) are a key tool for solving problems in real algebraic geometry and beyond. We recently presented a new CAD algorithm combining two advances: truth-table invariance, making the CAD invariant with…
Full binary trees naturally represent commutative non-associative products. There are many important examples of these products: finite-precision floating-point addition and NAND gates, among others. Balance in such a tree is highly…
We construct and study new generalisations to rooted trees and forests of some properties of shuffles of words. First, we build a coproduct on rooted trees which, together with their shuffle, endow them with bialgebra structure. We then…
We generalise the insertion into a binary heap to any directed acyclic graph (DAG) with one source vertex. This lets us formulate a general method for converting any such DAG into a data structure with priority queue interface. We apply our…
Perfect sorting by reversals, a problem originating in computational genomics, is the process of sorting a signed permutation to either the identity or to the reversed identity permutation, by a sequence of reversals that do not break any…
While modern general-purpose computing systems have ample amounts of memory, it is still the case that embedded computer systems, such as in a refrigerator, are memory limited; hence, such embedded systems motivate the need for strictly…
We consider systems of recursively defined combinatorial structures. We give algorithms checking that these systems are well founded, computing generating series and providing numerical values. Our framework is an articulation of the…
We continue the study of selection and sorting of $n$ numbers under the adversarial comparator model, where comparisons can be adversarially tampered with if the arguments are sufficiently close. We derive a randomized sorting algorithm…
Sorting is a foundational problem in computer science that is typically employed on sequences or total orders. More recently, a more general form of sorting on partially ordered sets (or posets), where some pairs of elements are…
Algorithms for embedding certain types of nilpotent subalgebras in maximal subalgebras of the same type are developed, using methods of real algebraic groups. These algorithms are applied to determine non-conjugate subalgebras of the…
We show that the theory of sorting by reversals fits into the well-established theory of circuit partitions of 4-regular multigraphs (which also involves the combinatorial structures of circle graphs and delta-matroids). In this way, we…
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 and ranking supervision is a method for training neural networks end-to-end based on ordering constraints. That is, the ground truth order of sets of samples is known, while their absolute values remain unsupervised. For that, we…
This article introduces an adaptive sorting algorithm that can relocate elements accurately by substituting their values into a function which we name it the guessing function. We focus on building this function which is the mapping…