| Summary: | 碩士 === 國立東華大學 === 資訊工程學系 === 90 === Given a graph, finding an optimal vertex ranking and constructing minimum height
elimination trees are interesting computational problems. The problem of finding the
minimum height elimination trees has been shown to be NP-hard on general graphs.
An optimal vertex ranking does not by itself provide enough information to construct
an elimination tree of minimum height. On the other hand, an optimal vertex ranking
can readily be found directly from an elimination tree of minimum height.
On trees, the optimal vertex ranking problem already has a linear-time algorithm
in the literature. However, there is no Linear-time algorithm for the problem of
finding minimum height elimination trees. A naive algorithm for this problem requires
O(n log n) time.
In this thesis, we propose a linear-time algorithm for constructing a minimum
height elimination tree of a tree.
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