Related papers: The technique of in-place associative sorting

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…

In sorting literature, comparative statics for multidimensional assignment models with general output functions and input distributions is an important open question. We provide a complete theory of comparative statics for technological…

In this paper we present theory and algorithms enabling classes of Artificial Intelligence (AI) systems to continuously and incrementally improve with a-priori quantifiable guarantees - or more specifically remove classification errors -…

Information inflow into a computational system is by a sequence of information items. Cognitive computing, i.e. performing transformations along that sequence, requires to represent item information as well as sequential information. Among…

The performance of value classes is highly dependent on how they are represented in the virtual machine. Value class instances are immutable, have no identity, and can only refer to other value objects or primitive values and since they…

Clustering is a popular machine learning technique for data mining that can process and analyze datasets to automatically reveal sample distribution patterns. Since the ubiquitous categorical data naturally lack a well-defined metric space…

We investigate the complexity of sorting in the model of sequential quantum circuits. While it is known that in general a quantum algorithm based on comparisons alone cannot outperform classical sorting algorithms by more than a constant…

Existing attention mechanisms are trained to attend to individual items in a collection (the memory) with a predefined, fixed granularity, e.g., a word token or an image grid. We propose area attention: a way to attend to areas in the…

The problem of ranking can be described as follows. We have a set of combinatorial objects $S$, such as, say, the k-subsets of n things, and we can imagine that they have been arranged in some list, say lexicographically, and we want to…

We present an unsupervised representation learning approach using videos without semantic labels. We leverage the temporal coherence as a supervisory signal by formulating representation learning as a sequence sorting task. We take…

Indexing intervals is a fundamental problem, finding a wide range of applications. Recent work on managing large collections of intervals in main memory focused on overlap joins and temporal aggregation problems. In this paper, we propose…

Items in many datasets can be arranged to a natural order. Such orders are useful since they can provide new knowledge about the data and may ease further data exploration and visualization. Our goal in this paper is to define a…

Sequential word order is important when processing text. Currently, neural networks (NNs) address this by modeling word position using position embeddings. The problem is that position embeddings capture the position of individual words,…

As a kind of basic machine learning method, clustering algorithms group data points into different categories based on their similarity or distribution. We present a clustering algorithm by finding hyper-planes to distinguish the data…

Neural algorithmic reasoning is an emerging area of machine learning focusing on building models that can imitate the execution of classic algorithms, such as sorting, shortest paths, etc. One of the main challenges is to learn algorithms…

This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some of the output variables are also input variables, linked by a linear dependency. Fundamental examples…

We extend the capabilities of neural networks by coupling them to external memory resources, which they can interact with by attentional processes. The combined system is analogous to a Turing Machine or Von Neumann architecture but is…

Set intersection is a fundamental operation in information retrieval and database systems. This paper introduces linear space data structures to represent sets such that their intersection can be computed in a worst-case efficient way. In…

This paper studies the average complexity on the number of comparisons for sorting algorithms. Its information-theoretic lower bound is $n \lg n - 1.4427n + O(\log n)$. For many efficient algorithms, the first $n\lg n$ term is easy to…

We introduce a quantitative method to compare arbitrary pairs of graph centrality measures, based on the ordering of vertices induced by them. The proposed method is conceptually simple, mathematically elegant, and allows for a quantitative…