Hicks, Illya V.2011-07-252011-07-252010Ma, Jing. "Branch-decomposition heuristics for linear matroids." (2010) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/62192">https://hdl.handle.net/1911/62192</a>.https://hdl.handle.net/1911/62192This thesis present two new heuristics which utilize classification and max-flow algorithm respectively to derive near-optimal branch-decompositions for linear matroids. In the literature, there are already excellent heuristics for graphs, however, no practical branch-decomposition methods for general linear matroids have been addressed yet. Introducing a "measure" which compares the "similarity" of elements of a linear matroid, this work reforms the linear matroid into a similarity graph. Then, two different methods, classification method and max-flow method, both basing on the similarity graph are developed into heuristics. Computational results using the classification method and the max-flow method on linear matroid instances are shown respectively.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Applied mathematicsMathematicsThesisTHESIS MATH.SCI. 2010 MA