Colored Spanning Graphs for Set Visualization
Year: 2016
Type: preprint
Abstract: We study an algorithmic problem that is motivated by ink minimization for sparse set visualizations. Our input is a set of points in the plane which are either blue, red, or purple. Blue points belong exclusively to the blue set, red points belong exclusively to the red set, and purple points belong to both sets. A \emph{red-blue-purple spanning graph} (RBP spanning graph) is a set of edges connecting the points such that the subgraph induced by the red and purple points is connected, and the subgraph induced by the blue and purple points is connected. We study the geometric properties of minimum RBP spanning graphs and the algorithmic problems associated with computing them. Specifically, we show that the general problem can be solved in polynomial time using matroid techniques. In addition, we discuss more efficient algorithms for the case in which points are located on a line or a circle, and also describe a fast $(\frac 12ρ+1)$-approximation algorithm, where $ρ$ is the Steiner ratio.
Source: arXiv (Cornell University)
Language: English
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funders: Ministry of Education, Culture, Sports, Science and Technology, Nederlandse Organisatie voor Wetenschappelijk Onderzoek, Center for Research and Development in Mathematics and Applications, Japan Society for the Promotion of Science, Fundação para a Ciência e a Tecnologia, Japan Science and Technology Agency, European Social Fund, Exploratory Research for Advanced Technology
Awards: Development of Approximation Algorithms with Theoretical Guarantee for Integer Programming Problem with Nonlinear Constraint, G1795024109, Projecto Estratégico - UI 4106 - 2014, G3315582433, Theory and Applications of Kinetic Computational Geometry with Uncertanity, G4600311389, G4921736922, G6383169256, G6401719457, G669834797, Challenging Research to Kinetic Adhoc Network Design, G8407736463
OpenAlex ID: W2949309673