Related papers: Algorithmic and combinatorial methods for enumerat…
Finding the k-medianin a network involves identifying a subset of k vertices that minimize the total distance to all other vertices in a graph. This problem has been extensively studied in computer science, graph theory, operations…
A team consisting of an unknown number of mobile agents, starting from different nodes of an unknown network, possibly at different times, have to meet at the same node. Agents are anonymous (identical), execute the same deterministic…
One widespread procedure to render the attractor of Kleinian groups, published in the renown book "Indra's Pearls" and based upon a combinatorial tree model, wants huge memory resources to compute and store all the words required. We will…
This is an introduction to the Atlas of Lie Groups and Representations software, for computing representation and structure theory of real reductive groups. The user is led through the basic commands of the software, via numerous examples.…
We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…
In this paper we give an algorithm to determine all finite matrix groups over a number field. Our algorithm is based on the representation theory of finite groups.
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…
This article discusses some difficulties in the implementation of combinatorial algorithms associated with the choice of all elements with certain properties among the elements of a set with great cardinality.The problem has been resolved…
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…
We survey several notions of Mackey functors and biset functors found in the literature and prove some old and new theorems comparing them. While little here will surprise the experts, we draw a conceptual and unified picture by making…
Enumerating matchings is a classical problem in the field of enumeration algorithms. There are polynomial-delay enumeration algorithms for several settings, such as enumerating perfect matchings, maximal matchings, and (weighted) matchings…
Given a system of equations in a "random" finitely generated subgroup of the braid group, we show how to find a small ordered list of elements in the subgroup, which contains a solution to the equations with a significant probability.…
We develop the rudiments of a finite-dimensional representation theory of groups over idempotent semifields by considering linear actions on tropical linear spaces. This can be considered a tropical representation theory, a characteristic…
Quiver representations arise naturally in many areas across mathematics. Here we describe an algorithm for calculating the vector space of sections, or compatible assignments of vectors to vertices, of any finite-dimensional representation…
The computation of a maximal order of an order in a semisimple algebra over a global field is a classical well-studied problem in algorithmic number theory. In this paper we consider the related problems of computing all minimal overorders…
We give a uniform explicit construction of finite two-generator presentations for the special linear groups over the integers in all ranks at least three. The construction builds on the generating-pair work of Conder--Liversidge--Vsemirnov…
Many fundamental NP-hard problems can be formulated as integer linear programs (ILPs). A famous algorithm by Lenstra solves ILPs in time that is exponential only in the dimension of the program, and polynomial in the size of the ILP. That…
We give two algorithms to compute linear determinantal representations of smooth plane curves of any degree over any field. As particular examples, we explicitly give representatives of all equivalence classes of linear determinantal…
Let $G$ be a finite solvable group. Then $G$ always has a useful presentation, which we call a "long presentation". Using a "long presentation" of $G$, we present an inductive method of constructing the irreducible representations of $G$…
Let k be an imaginary quadratic number field (with class number 1). We describe a new, essentially linear-time algorithm, to list all isomorphism classes of cubic extensions L/k up to a bound X on the norm of the relative discriminant…