Tree transformation through vertex contraction with application to skeletons

Authors:
Arseny Smirnov;Kira Vyatkina
Affiliations:
Saint Petersburg State University, Dept. of Mathematics and Mechanics, Saint Petersburg, Russia;Saint Petersburg State University, Dept. of Mathematics and Mechanics, Saint Petersburg, Russia
Venue:
ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part III
Year:
2011

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Abstract

We start with the problem of verifying e-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.