dc.contributor.author Ruiz Velázquez, Lesvia Elena dc.date.accessioned 2010-09-08 15:17:22 (GMT) dc.date.available 2010-09-08 15:17:22 (GMT) dc.date.issued 2010-09-08T15:17:22Z dc.date.submitted 2010 dc.identifier.uri http://hdl.handle.net/10012/5481 dc.description.abstract This thesis deals with planar drawings of planar graphs such that each interior face has en a prescribed area. Our work is divided into two main sections. The rst one deals with straight-line drawings and the second one with orthogonal drawings. For straight-line drawings, it was known that such drawings exist for all planar graphs with maximum degree 3. We show here that such drawings exist for all planar partial 3-trees, i.e., subgraphs of a triangulated planar graph obtained by repeatedly inserting a vertex in one triangle and connecting it to all vertices of the triangle. Moreover, vertices have rational coordinates if the face areas are rational, and we can bound the resolution. For orthogonal drawings, we give an algorithm to draw triconnected planar graphs with maximum degree 3. This algorithm produces a drawing with at most 8 bends per face and 4 bends per edge, which improves the previous known result of 34 bends per face. Both vertices and bends have rational coordinates if the face areas are rational. dc.language.iso en en dc.publisher University of Waterloo en dc.subject graph drawing en dc.subject planar en dc.subject prescribed face area en dc.title Drawing planar graphs with prescribed face areas en dc.type Master Thesis en dc.comment.hidden Part of this thesis was published in Graph Drawing 2009. Permission has been obtained from the publisher, they didn't ask for written permission to be in the thesis. They just asked for the publication to be mentioned in the references section, which has been done. en dc.pending false en dc.subject.program Computer Science en uws-etd.degree.department School of Computer Science en uws-etd.degree Master of Mathematics en uws.typeOfResource Text en uws.peerReviewStatus Unreviewed en uws.scholarLevel Graduate en
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