Related papers: Logspace computations in graph products

Sofic shifts are symbolic dynamical systems defined by the set of bi-infinite sequences on an edge-labeled directed graph, called a presentation. We study the computational complexity of an array of natural decision problems about…

Explaining neural network models is important for increasing their trustworthiness in real-world applications. Most existing methods generate post-hoc explanations for neural network models by identifying individual feature attributions or…

In this work, we study the problems of counting and sampling Mazurkiewicz traces that a regular language touches. Fix an alphabet $\Sigma$ and an independence relation $\mathbb{I} \subseteq \Sigma \times \Sigma$. The input consists of a…

While graphs and abstract data structures can be large and complex, practical instances are often regular or highly structured. If the instance has sufficient structure, we might hope to compress the object into a more succinct…

Estimating the structure of directed acyclic graphs (DAGs, also known as Bayesian networks) is a challenging problem since the search space of DAGs is combinatorial and scales superexponentially with the number of nodes. Existing approaches…

We generalize the classical construction principles of infinite-dimensional real (and complex) Lie groups to the case of Lie groups over non-discrete topological fields. In particular, we discuss linear Lie groups, mapping groups, test…

Graph aggregation is the process of computing a single output graph that constitutes a good compromise between several input graphs, each provided by a different source. One needs to perform graph aggregation in a wide variety of…

Finding, counting and/or listing triangles (three vertices with three edges) in large graphs are natural fundamental problems, which received recently much attention because of their importance in complex network analysis. We provide here a…

While spectral clustering algorithms for undirected graphs are well established and have been successfully applied to unsupervised machine learning problems ranging from image segmentation and genome sequencing to signal processing and…

In this paper we develop the theory of train track maps on graphs of groups. Expanding a definition of Bass, we define a notion of a map of a graph of groups, and of a homotopy equivalence. We prove that under one of two technical…

We propose a new cryptosystem based on polycyclic groups. The cryptosystem is based on the fact that the word problem can be solved effectively in polycyclic groups, while the known solutions to the conjugacy problem are far less efficient.

It is known that the bounded Geodesic Length Problem in free metabelian groups is NP-complete (in particular, the Geodesic Problem is NP-hard). We construct a 2-approximation polynomial time deterministic algorithm for the Geodesic Problem.…

This thesis deals with applications of experimental mathematics to a number of problems. The first problem is related to random graph statistics. We consider a certain class of Galton-Watson random trees and look at the total height…

We prove a complexity dichotomy theorem for Holant Problems on 3-regular graphs with an arbitrary complex-valued edge function. Three new techniques are introduced: (1) higher dimensional iterations in interpolation; (2) Eigenvalue Shifted…

This paper is dedicated to the conjugacy problem in $GL(n,\Z)$ and its connection with algebraic number theory. This connection may be summed up in the Latimer-MacDuffee-Taussky Theorem, which, in a very broad sense, identifies the…

This paper reviews the moment graph technique that allows to translate certain representation theoretic problems into geometric ones. For simplicity we restrict ourselves to the case of semisimple complex Lie algebras. In particular, we…

As a supplement to my talk at the workshop, this extended abstract motivates and summarizes my work with co-authors on problems in two separate areas: first, in the lambda-calculus with letrec, a universal model of computation, and second,…

Current graph neural networks (GNNs) lack generalizability with respect to scales (graph sizes, graph diameters, edge weights, etc..) when solving many graph analysis problems. Taking the perspective of synthesizing graph theory programs,…

Current applications have produced graphs on the order of hundreds of thousands of nodes and millions of edges. To take advantage of such graphs, one must be able to find patterns, outliers and communities. These tasks are better performed…

We prove a complexity dichotomy theorem for a class of Holant problems on planar 3-regular bipartite graphs. The complexity dichotomy states that for every weighted constraint function $f$ defining the problem (the weights can even be…