A Survey on the Steiner Forest Problem

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Negahbani, Maryam | 2017

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 49489 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Foroughmand-Arabi, Mohammad Hadi
Abstract:
The Steiner forest problem is one of the most fundamental issues in network design that emerges in various contexts, such as the design of communication networks,transportation networks, VLSI circuits and phylogenetic network reconstruction. In this problem, we are given a connected weighted undirected graph and a special subset of vertices that are partitioned in pairs. The goal is to fnd a minimum-cost sub-graph in which each special vertex is connected to its mate. In this thesis we review a set of selected solutions for this problem and a few other related problems.For example, we study modeling and solving the s-t shortest path problem in order to gain insight into current Steiner forest models. Moreover, we investigate undirectedcut and lifted-cut relaxations along with AKR and KLS algorithms which are the most accurate schemes for approximating the Steiner forest so far. In the end, we present a new linear relaxation for modeling the problem and analyze its properties
Keywords:
Shortest Path ; Primal-Dual Algorithm ; Approximate Algorithm ; Steiner Forest ; Linear Relaxation