Related papers: Sorting and generating reduced words
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},…
A monoid $M$ generated by a set $S$ of symbols can be described as the set of equivalence classes of finite words in $S$ under some relations that specify when some contiguous sequence of symbols can be replaced by another. If $a,b\in S$, a…
We investigate the generalisation of quantum search of unstructured and totally ordered sets to search of partially ordered sets (posets). Two models for poset search are considered. In both models, we show that quantum algorithms can…
It is often useful to sort words into an order that reflects relations among their meanings as obtained by using a thesaurus. In this paper, we introduce a method of arranging words semantically by using several types of `{\sf is-a}'…
A wide range of applications, most notably in comparative genomics, involve the computation of a shortest sorting sequence of operations for a given permutation, where the set of allowed operations is fixed beforehand. Such sequences are…
We find large lower bounds for a certain family of algorithms, and prove that such bounds are limited only by natural computability arguments.
The election is a classical problem in distributed algorithmic. It aims to design and to analyze a distributed algorithm choosing a node in a graph, here, in a tree. In this paper, a class of randomized algorithms for the election is…
Text coherence is a fundamental problem in natural language generation and understanding. Organizing sentences into an order that maximizes coherence is known as sentence ordering. This paper is proposing a new approach based on the graph…
A simple method to produce a random order type is to take the order type of a random point set. We conjecture that many probability distributions on order types defined in this way are heavily concentrated and therefore sample inefficiently…
An attractive mechanism to specify global constraints in rostering and other domains is via formal languages. For instance, the Regular and Grammar constraints specify constraints in terms of the languages accepted by an automaton and a…
Distributed optimization is fundamental to modern machine learning applications like federated learning, but existing methods often struggle with ill-conditioned problems and face stability-versus-speed tradeoffs. We introduce fractional…
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,…
Data-driven segmentation of words into subword units has been used in various natural language processing applications such as automatic speech recognition and statistical machine translation for almost 20 years. Recently it has became more…
Motivated by the development of computer theory, the sorting algorithm is emerging in an endless stream. Inspired by decrease and conquer method, we propose a brand new sorting algorithmUltimately Heapsort. The algorithm consists of two…
Comparison-based algorithms are algorithms for which the execution of each operation is solely based on the outcome of a series of comparisons between elements. Comparison-based computations can be naturally represented via the following…
In this paper we introduce a word embedding composition method based on the intuitive idea that a fair embedding representation for a given set of words should satisfy that the new vector will be at the same distance of the vector…
Generating trees are a useful technique in the enumeration of various combinatorial objects, particularly restricted permutations. Quite often the generating tree for the set of permutations avoiding a set of patterns requires infinitely…
Sorting input objects is an important step in many machine learning pipelines. However, the sorting operator is non-differentiable with respect to its inputs, which prohibits end-to-end gradient-based optimization. In this work, we propose…
Dependency distance minimization (DDm) is a well-established principle of word order. It has been predicted theoretically that DDm implies compression, namely the minimization of word lengths. This is a second order prediction because it…
It is known that the Wadge reducibility of regular $\omega$-languages is efficiently decidable (Krishnan et al., 1995), (Wilke, Yoo, 1995). In this paper we study analogous problem for regular k-partitions of $\omega$-languages. In the…