dc.contributor.author Grout, Logan dc.date.accessioned 2020-09-02 17:56:26 (GMT) dc.date.available 2020-09-02 17:56:26 (GMT) dc.date.issued 2020-09-02 dc.date.submitted 2020-08-25 dc.identifier.uri http://hdl.handle.net/10012/16229 dc.description.abstract This thesis focuses on the Node-Connectivity Tree Augmentation Problem (NC-TAP), formally defined as follows. The first input of the problem is a graph G which has vertex set V and edge set E. We require |V| >= 3 to avoid degenerate cases. The edge set E is a disjoint union of two sets T and L where the subgraph (V,T) is connected and acyclic. We call the edges in T the tree edges and the edges in L are called links. The second input is a vector c in R^L, c >= 0 (a vector of nonnegative real numbers indexed by the links), which is called the cost of the links. We often refer to this graph G and cost vector c as an instance of NC-TAP. Given an instance G = (V, T U L) and c to NC-TAP, a feasible solution to that instance is a set of links F such that the graph (V, T U F) is 2-connected. The cost of a set of links. The goal of NC-TAP is to find a feasible solution F^* to the given instance such that the the cost of F^* is minimum among all feasible solutions to the instance. en This thesis is mainly expository and it has two goals. First, we present the current best-known algorithms for NC-TAP. The second goal of this thesis is to explore new directions in the study of NC-TAP in the last chapter. This is an exploratory chapter where the goal is to use the state of the art techniques for TAP to develop an algorithm for NC-TAP which has an approximation guarantee better than factor 2. dc.language.iso en en dc.publisher University of Waterloo en dc.subject combinatorial optimization en dc.subject tree augmentation en dc.title Augmenting Trees to Achieve 2-Node-Connectivity en dc.type Master Thesis en dc.pending false uws-etd.degree.department Combinatorics and Optimization en uws-etd.degree.discipline Combinatorics and Optimization en uws-etd.degree.grantor University of Waterloo en uws-etd.degree Master of Mathematics en uws.contributor.advisor Cheriyan, Joseph 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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