Related papers: Graph-Theoretic Solutions to Computational Geometr…
One of the most useful measures of cluster quality is the modularity of a partition, which measures the difference between the number of the edges joining vertices from the same cluster and the expected number of such edges in a random…
Spectral graph theory is well known and widely used in computer vision. In this paper, we analyze image segmentation algorithms that are based on spectral graph theory, e.g., normalized cut, and show that there is a natural connection…
Graph theoretical problems based on shortest paths are at the core of research due to their theoretical importance and applicability. This paper deals with the geodetic number which is a global measure for simple connected graphs and it…
The notion of graph covers (also referred to as locally bijective homomorphisms) plays an important role in topological graph theory and has found its computer science applications in models of local computation. For a fixed target graph…
We introduce a new formalism and a number of new results in the context of geometric computational vision. The classical scope of the research in geometric computer vision is essentially limited to static configurations of points and lines…
In the field of complex networks and graph theory, new results are typically tested on graphs generated by a variety of algorithms such as the Erd\H{o}s-R\'{e}nyi model or the Barab\'{a}si-Albert model. Unfortunately, most graph generating…
In a previous work of the authors, a result to algorithmically compute the topology types of the level curves of an algebraic surface, is given. From this result, here we derive applications based on level curves to determine some…
A theoretical performance analysis of the graph neural network (GNN) is presented. For classification tasks, the neural network approach has the advantage in terms of flexibility that it can be employed in a data-driven manner, whereas…
Given a collection of planar graphs $G_1,\dots,G_k$ on the same set $V$ of $n$ vertices, the simultaneous geometric embedding (with mapping) problem, or simply $k$-SGE, is to find a set $P$ of $n$ points in the plane and a bijection $\phi:…
While Annealing Machines (AM) have shown increasing capabilities in solving complex combinatorial problems, positioning themselves as a more immediate alternative to the expected advances of future fully quantum solutions, there are still…
The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…
Vertex connectivity and edge connectivity are fundamental concepts in graph theory that have been widely studied from both structural and algorithmic perspectives. The focus of this paper is on computing these two parameters for graphs…
Graph polynomials encode fundamental combinatorial invariants of graphs. Their computation is investigated using tree and path decomposition frameworks, with formal definitions of treewidth, k-trees, and pathwidth establishing the…
We use a well known problem in discrete and computational geometry (partitions of measures by $k$-fans) as a motivation and as a point of departure to illustrate many aspects, both theoretical and computational, of the problem of…
We investigate the problem of constructing planar drawings with few bends for two related problems, the partially embedded graph problem---to extend a straight-line planar drawing of a subgraph to a planar drawing of the whole graph---and…
We state the graph-theoretic computational problem of finding tight paths in a directed, edge-weighted graph, as well as its simplification of finding tight pairs. These problems are motivated by the need of algorithms that find so-called…
Grouping the nodes of a graph into clusters is a standard technique for studying networks. We study a problem where we are given a directed network and are asked to partition the graph into a sequence of coherent groups. We assume that…
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…
Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study the…
This chapter presents an introduction to graph colouring algorithms. The focus is on vertex-colouring algorithms that work for general classes of graphs with worst-case performance guarantees in a sequential model of computation. The…