Browsing Mathematics (Faculty of) by Supervisor "Lubiw, Anna"
Now showing items 1-8 of 8
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Algorithms for Geometric Facility Location: Centers in a Polygon and Dispersion on a Line
(University of Waterloo, 2023-02-24)We study three geometric facility location problems in this thesis. First, we consider the dispersion problem in one dimension. We are given an ordered list of (possibly overlapping) intervals on a line. We wish to choose ... -
Building a larger class of graphs for efficient reconfiguration of vertex colouring
(University of Waterloo, 2020-05-13)A $k$-colouring of a graph $G$ is an assignment of at most $k$ colours to the vertices of $G$ so that adjacent vertices are assigned different colours. The reconfiguration graph of the $k$-colourings, $\mathcal{R}_k(G)$, ... -
Computing Realistic Terrains from Imprecise Elevations
(University of Waterloo, 2022-04-19)It is ideal for triangulated terrains to have characteristics or properties that are realistic. In the imprecise terrain model, each vertex of a triangulated terrain has an imprecise eleva- tion value only known to lie ... -
Connectivity Properties of the Flip Graph After Forbidding Triangulation Edges
(University of Waterloo, 2022-09-23)The flip graph for a set $P$ of points in the plane has a vertex for every triangulation of $P$, and an edge when two triangulations differ by one flip that replaces one triangulation edge by another. The flip graph is ... -
A Faster Algorithm for Recognizing Edge-Weighted Interval Graphs
(University of Waterloo, 2017-04-27)Interval graphs—the intersection graphs of one-dimensional intervals—are considered one of the most useful mathematical structures to model real life applications. Interval graphs have been widely studied since they first ... -
Graph Morphing via Orthogonal Box Drawings
(University of Waterloo, 2023-12-18)Abstract: A graph is a set of vertices, with some pairwise connections given by a set of edges. A graph drawing, such as a node-link diagram, visualizes a graph with geometric features. One of the most common forms of a ... -
Minimum Shared-Power Edge Cut
(University of Waterloo, 2018-08-24)We introduce a problem called the Minimum Shared-Power Edge Cut (MSPEC). The input to the problem is an undirected edge-weighted graph with distinguished vertices s and t, and the goal is to find an s-t cut by assigning ... -
Straight Line Movement in Morphing and Pursuit Evasion
(University of Waterloo, 2017-10-24)Piece-wise linear structures are widely used to define problems and to represent simplified solutions in computational geometry. A piece-wise linear structure consists of straight-line or linear pieces connected together ...