We provide an algorithm for computing a planar morph between any two planar straight-line drawings of any n-vertex plane graph in O(n) morphing steps, thus improving upon the previously best known O(n2) upper bound. Further, we prove that our algorithm is optimal, that is, we show that there exist two planar straight-line drawings Γs and Γt of an n-vertex plane graph G such that any planar morph between Γs and Γt requires Ω(n) morphing steps.
@article{arxiv.1402.4364,
title = {Morphing Planar Graph Drawings Optimally},
author = {Patrizio Angelini and Giordano Da Lozzo and Giuseppe Di Battista and Fabrizio Frati and Maurizio Patrignani and Vincenzo Roselli},
journal= {arXiv preprint arXiv:1402.4364},
year = {2014}
}