This 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.
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