Tree Transformation through Vertex Contraction with Application to Skeletons
We start with the problem of verifying ε-equivalence between the medial and a linear axes for a simple polygon, and restate it as a problem of transforming a tree with labeled leaved into another one through contraction of inner vertices in presence of certain restrictions. We demonstrate that a possibility to contract non-adjacent vertices is sometimes crucial for the initial task.
Next, we provide a linear algorithm for solving a relaxed problem on trees, when any two inner vertices may be glued together. We further show that if a required transformation of a given tree can be performed, then it can also be accomplished in such a way that after each contraction, the obtained intermediate graph is a tree, and the respective sequence of merges can be retrieved in linear time.
KeywordsAdjacent Vertex Medial Axis Simple Polygon Matching Coloring Geometric Graph
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