Related papers: Applications of substring searching to group prese…

We describe a substring search problem that arises in group presentation simplification processes. We suggest a two-level searching model: skip and match levels. We give two timestamp algorithms which skip searching parts of the text where…

Understanding the similar properties of people involved in group search sessions has the potential to significantly improve collaborative search systems; such systems could be enhanced by information retrieval algorithms and user interface…

Computer based techniques for recognizing finitely presented groups are quite powerful. Tools available for this purpose are outlined. They are available both in stand-alone programs and in more comprehensive systems. A general…

Subgroup-discovery methods allow users to obtain simple descriptions of interesting regions in a dataset. Using constraints in subgroup discovery can enhance interpretability even further. In this article, we focus on two types of…

We address the problem of counting the number of strings in a collection where a given pattern appears, which has applications in information retrieval and data mining. Existing solutions are in a theoretical stage. We implement these…

Peer-grouping is used in many sectors for organisational learning, policy implementation, and benchmarking. Clustering provides a statistical, data-driven method for constructing meaningful peer groups, but peer groups must be compatible…

Finding a suitable data representation for a specific task has been shown to be crucial in many applications. The success of subspace clustering depends on the assumption that the data can be separated into different subspaces. However,…

Strings form a fundamental data type in computer systems. String searching has been extensively studied since the inception of computer science. Increasingly many applications have to deal with imprecise strings or strings with fuzzy…

This is a survey of results on random group presentations, and on random subgroups of certain fixed groups. Being a survey, this paper does not contain new results, but it offers a synthetic view of a part of this very active field of…

While advances in computing resources have made processing enormous amounts of data possible, human ability to identify patterns in such data has not scaled accordingly. Efficient computational methods for condensing and simplifying data…

We describe a new type of polycyclic presentations, that we will call refined solvable presentations, for polycyclic groups. These presentations are obtained by refining a series of normal subgroups with abelian sections. These…

Self-similar groups provide a rich source of groups with interesting properties; e.g., infinite torsion groups (Burnside groups) and groups with an intermediate word growth. Various self-similar groups can be described by a recursive…

We introduce a new technique for the efficient management of large sequences of multidimensional data, which takes advantage of regularities that arise in real-world datasets and supports different types of aggregation queries. More…

Graphs may be used to represent many different problem domains -- a concrete example is that of detecting communities in social networks, which are represented as graphs. With big data and more sophisticated applications becoming widespread…

Recent work on explainable clustering allows describing clusters when the features are interpretable. However, much modern machine learning focuses on complex data such as images, text, and graphs where deep learning is used but the raw…

Improving the explainability of the results from machine learning methods has become an important research goal. Here, we study the problem of making clusters more interpretable by extending a recent approach of [Davidson et al., NeurIPS…

Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational…

Computational models of human language often involve combinatorial problems. For instance, a probabilistic parser may marginalize over exponentially many trees to make predictions. Algorithms for such problems often employ dynamic…

Graph simulation (using graph schemata or data guides) has been successfully proposed as a technique for adding structure to semistructured data. Design patterns for description (such as meta-classes and homomorphisms between schema…

The problem of storing a set of strings --- a string dictionary --- in compact form appears naturally in many cases. While classically it has represented a small part of the whole data to be processed (e.g., for Natural Language processing…