Distance Measures for Embedded Graphs
Abstract
We introduce new distance measures for comparing straightline embedded graphs based on the Fréchet distance and the weak Fréchet distance. These graph distances are defined using continuous mappings and thus take the combinatorial structure as well as the geometric embeddings of the graphs into account. We present a general algorithmic approach for computing these graph distances. Although we show that deciding the distances is NPhard for general embedded graphs, we prove that our approach yields polynomial time algorithms if the graphs are trees, and for the distance based on the weak Fréchet distance if the graphs are planar embedded. Moreover, we prove that deciding the distances based on the Fréchet distance remains NPhard for planar embedded graphs and show how our general algorithmic approach yields an exponential time algorithm and a polynomial time approximation algorithm for this case.
 Publication:

arXiv eprints
 Pub Date:
 December 2018
 arXiv:
 arXiv:1812.09095
 Bibcode:
 2018arXiv181209095A
 Keywords:

 Computer Science  Computational Geometry
 EPrint:
 27 pages, 14 Figures