- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- UBC Theses and Dissertations /
- On path-greedy geometric spanners
Open Collections
UBC Theses and Dissertations
UBC Theses and Dissertations
On path-greedy geometric spanners Morais de Arruda Siaudzionis, Lucca
Abstract
A t-spanner is a graph in which the shortest path between two vertices never exceeds t times the distance between the two nodes – a t-approximation of the complete graph. A geometric graph is one in which its vertices are points with defined coordinates and the edges correspond to line segments between them with a distance function, such as Euclidean distance. Geometric spanners are used to design networks of reduced complexity, optimizing metrics such as the planarity or degree of the graph. One famous algorithm used to generate spanners is path-greedy, which scans pairs of points in non-decreasing order of distance and adds the edge between them unless the current set of added edges already connects them with a path that t-approximates the edge length. Graphs from this algorithm are called path-greedy spanners. This work analyzes properties of path-greedy geometric spanners under different conditions. Specifically, we answer an open problem regarding the planarity and degree of path-greedy 5.19-spanners in convex point sets, and explore how the algorithm behaves under random tiebreaks for grid point sets. Lastly, we show a simple and efficient way to reduce the degree of a plane spanner by adding extra points.
Item Metadata
Title |
On path-greedy geometric spanners
|
Creator | |
Supervisor | |
Publisher |
University of British Columbia
|
Date Issued |
2021
|
Description |
A t-spanner is a graph in which the shortest path between two vertices never exceeds t times the distance between the two nodes – a t-approximation of the complete graph. A geometric graph is one in which its vertices are points with defined coordinates and the edges correspond to line segments between them with a distance function, such as Euclidean distance. Geometric spanners are used to design networks of reduced complexity, optimizing metrics such as the planarity or degree of the graph.
One famous algorithm used to generate spanners is path-greedy, which scans pairs of points in non-decreasing order of distance and adds the edge between them unless the current set of added edges already connects them with a path that t-approximates the edge length. Graphs from this algorithm are called path-greedy spanners. This work analyzes properties of path-greedy geometric spanners under different conditions.
Specifically, we answer an open problem regarding the planarity and degree of path-greedy 5.19-spanners in convex point sets, and explore how the algorithm behaves under random tiebreaks for grid point sets. Lastly, we show a simple and efficient way to reduce the degree of a plane spanner by adding extra points.
|
Genre | |
Type | |
Language |
eng
|
Date Available |
2021-09-16
|
Provider |
Vancouver : University of British Columbia Library
|
Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
DOI |
10.14288/1.0402167
|
URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
|
Graduation Date |
2021-11
|
Campus | |
Scholarly Level |
Graduate
|
Rights URI | |
Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International