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dc.contributor.authorDemontigny, Philippe 15:14:32 (GMT) 15:14:32 (GMT)
dc.description.abstractIn 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.publisherUniversity of Waterlooen
dc.subjectApproximation Algorithmen
dc.subjectOuterplanar Graphen
dc.subjectLayered Drawingen
dc.subjectUmbrella Systemen
dc.subjectUmbrella Depthen
dc.subjectFlat Visibility Representationen
dc.titleA 2-Approximation for the Height of Maximal Outerplanar Graph Drawingsen
dc.typeMaster Thesisen
dc.pendingfalse R. Cheriton School of Computer Scienceen Scienceen of Waterlooen
uws-etd.degreeMaster of Mathematicsen
uws.contributor.advisorBiedl, Therese
uws.contributor.affiliation1Faculty of Mathematicsen

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