dc.contributor.author Razaghpour, Mina dc.date.accessioned 2008-09-26 16:08:32 (GMT) dc.date.available 2008-09-26 16:08:32 (GMT) dc.date.issued 2008-09-26T16:08:32Z dc.date.submitted 2008 dc.identifier.uri http://hdl.handle.net/10012/4055 dc.description.abstract This thesis examines the (geometric) Steiner tree problem: Given a set of points P in the plane, find a shortest tree interconnecting all points in P, with the possibility of adding points outside P, called the Steiner points, as additional vertices of the tree. The Steiner tree problem has been studied in different metric spaces. In this thesis, we study the problem in Euclidean and rectilinear metrics. en One of the most natural heuristics for the Steiner tree problem is to use a minimum spanning tree, which can be found in O(nlogn) time . The performance ratio of this heuristic is given by the Steiner ratio, which is defined as the minimum possible ratio between the lengths of a minimum Steiner tree and a minimum spanning tree. We survey the background literature on the Steiner ratio and study the generalization of the Steiner ratio to the case of obstacles. We introduce the concept of an anchored Steiner tree: an obstacle-avoiding Steiner tree in which the Steiner points are only allowed at obstacle corners. We define the obstacle-avoiding Steiner ratio as the ratio of the length of an obstacle-avoiding minimum Steiner tree to that of an anchored obstacle-avoiding minimum Steiner tree. We prove that, for the rectilinear metric, the obstacle-avoiding Steiner ratio is equal to the traditional (obstacle-free) Steiner ratio. We conjecture that this is also the case for the Euclidean metric and we prove this conjecture for three points and any number of obstacles. dc.language.iso en en dc.publisher University of Waterloo en dc.subject Computer Science en dc.subject Computational geometry en dc.subject Steiner tree en dc.subject Steiner ratio en dc.title The Steiner Ratio for the Obstacle-Avoiding Steiner Tree Problem en dc.type Master Thesis 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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