dc.contributor.author Demontigny, Philippe dc.date.accessioned 2016-08-18 15:14:32 (GMT) dc.date.available 2016-08-18 15:14:32 (GMT) dc.date.issued 2016-08-18 dc.date.submitted 2016-08-11 dc.identifier.uri http://hdl.handle.net/10012/10652 dc.description.abstract In this thesis, we study drawings of maximal outerplanar graphs that place vertices on integer coordinates. We introduce a new class of graphs, called umbrellas, and a new method of splitting maximal outerplanar graphs into systems of umbrellas. By doing so, we generate a new graph parameter, called the umbrella depth (ud), that can be used to approximate the optimal height of a drawing of a maximal outerplanar graph. We show that for any maximal outerplanar graph G, we can create a flat visibility representation of G with height at most 2ud(G) + 1. This drawing can be transformed into a straight-line drawing of the same height. We then prove that the height of any drawing of G is at least ud(G) + 1, which makes our result a 2-approximation for the optimal height. The best previously known approximation algorithm gave a 4-approximation. In addition, we provide an algorithm for finding the umbrella depth of G in linear time. Lastly, we compare the umbrella depth to other graph parameters such as the pathwidth and the rooted pathwidth, which have been used in the past for outerplanar graph drawing algorithms. en dc.language.iso en en dc.publisher University of Waterloo en dc.subject Approximation Algorithm en dc.subject Outerplanar Graph en dc.subject Layered Drawing en dc.subject Umbrella en dc.subject Umbrella System en dc.subject Umbrella Depth en dc.subject Height en dc.subject Flat Visibility Representation en dc.title A 2-Approximation for the Height of Maximal Outerplanar Graph Drawings en dc.type Master Thesis en dc.pending false uws-etd.degree.department David R. Cheriton School of Computer Science en uws-etd.degree.discipline Computer Science en uws-etd.degree.grantor University of Waterloo en uws-etd.degree Master of Mathematics en uws.contributor.advisor Biedl, Therese uws.contributor.affiliation1 Faculty of Mathematics en uws.published.city Waterloo en uws.published.country Canada en uws.published.province Ontario en uws.typeOfResource Text en uws.peerReviewStatus Unreviewed en uws.scholarLevel Graduate en
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