Steiner tree problems on special planar graphs
Abstract
The Steiner Tree Problem (STP) on graphs seeks a minimum edge weight tree subgraph that spans a specified subset of vertices. It captures the combinatorial essence of many network design and distribution models in the same way that the traveling salesman problem abstracts the essential combinatorial structure of routing and sequencing. Although the STP is NP-Hard on planar graphs, it is known to be polynomially solvable on rich subclasses, including series-parallel and $\beta$-planar graphs. However, no one of these classes subsumes the other, and a polyhedral description, which would facilitate the transfer of results to harder cases, was previously known for only the series-parallel case. This research extends and unifies research on STP's and related questions. A polynomial algorithm is presented for a new class termed series-parallel block graphs that contains and significantly generalizes the other solvable classes. A generic, algorithm-based process for obtaining polyhedral characterizations is also developed that both yields a description for the full class of STP's on series-parallel block graphs and implies an analogous characterization for many similarly-solved combinatorial optimization problems.
Degree
Ph.D.
Advisors
Rardin, Purdue University.
Subject Area
Operations research
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