Related papers: Engineering Art Galleries
Orthogonal drawings, i.e., embeddings of graphs into grids, are a classic topic in Graph Drawing. Often the goal is to find a drawing that minimizes the number of bends on the edges. A key ingredient for bend minimization algorithms is the…
Creating and understanding art has long been a hallmark of human ability. When presented with finished digital artwork, professional graphic artists can intuitively deconstruct and replicate it using various drawing tools, such as the line…
New algorithms are devised for finding the maxima of multidimensional point samples, one of the very first problems studied in computational geometry. The algorithms are very simple and easily coded and modified for practical needs. The…
Designing and analyzing algorithms with provable performance guarantees enables efficient optimization problem solving in different application domains, e.g.\ communication networks, transportation, economics, and manufacturing. Despite the…
Schematic maps are in daily use to show the connectivity of subway systems and to facilitate travellers to plan their journeys effectively. This study surveys up-to-date algorithmic approaches in order to give an overview of the state of…
We study the problem of learning an unknown graph provided via an oracle using a quantum algorithm. We consider three query models. In the first model ("OR queries"), the oracle returns whether a given subset of the vertices contains any…
This paper describes several new problems and ideas concerning algebraic geometry and complexity theory. It first uses the idea of coloring graphs with elements of finite fields. This procedure then shows that graph coloring problems can be…
By any account, the 1998 proof of the Kepler conjecture is complex. The thesis underlying this article is that the proof is complex because it is highly under-automated. Throughout that proof, manual procedures are used where automated ones…
The presented material is devoted to the equivalent conversion from the vertex graphs to the edge graphs. We suggest that the proved theorems solve the problem of the isomorphism of graphs, the problem of the graph's enumeration with the…
The problem of extending partial geometric graph representations such as plane graphs has received considerable attention in recent years. In particular, given a graph $G$, a connected subgraph $H$ of $G$ and a drawing $\mathcal{H}$ of $H$,…
We study the problem of planning paths for a team of robots for visually monitoring an environment. Our work is motivated by surveillance and persistent monitoring applications. We are given a set of target points in a polygonal environment…
It has long been observed that for practically any computational problem that has been intensely studied, different instances are best solved using different algorithms. This is particularly pronounced for computationally hard problems,…
Many variations of the classical graph coloring model have been intensively studied due to their multiple applications; scheduling problems and aircraft assignments, for instance, motivate the robust coloring problem. This model gets to…
Algorithms have been fundamental to recent global technological advances and, in particular, they have been the cornerstone of technical advances in one field rapidly being applied to another. We argue that algorithms possess fundamentally…
Traditionally, numerical algorithms are seen as isolated pieces of code confined to an {\em in silico} existence. However, this perspective is not appropriate for many modern computational approaches in control, learning, or optimization,…
This paper provides an overview of modern digital geometry and topology through mathematical principles, algorithms, and measurements. It also covers recent developments in the applications of digital geometry and topology including image…
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…
We consider the selective graph coloring problem, which is a generalization of the classical graph coloring problem. Given a graph together with a partition of its vertex set into clusters, we want to choose exactly one vertex per cluster…
We consider the problem of embedding the nodes of a hypergraph into Euclidean space under the assumption that the interactions arose through closeness to unknown hyperedge centres. In this way, we tackle the inverse problem associated with…
Clustering artworks based on style can have many potential real-world applications like art recommendations, style-based search and retrieval, and the study of artistic style evolution of an artist or in an artwork corpus. We introduce and…