Succinct Greedy Drawings Do Not Always Exist
- Cite this paper as:
- Angelini P., Di Battista G., Frati F. (2010) Succinct Greedy Drawings Do Not Always Exist. In: Eppstein D., Gansner E.R. (eds) Graph Drawing. GD 2009. Lecture Notes in Computer Science, vol 5849. Springer, Berlin, Heidelberg
A greedy drawing is a graph drawing containing a distance-decreasing path for every pair of nodes. A path (v0,v1,...,vm) is distance-decreasing if d(vi,vm) < d(vi − 1,vm), for i = 1,...,m. Greedy drawings easily support geographic greedy routing. Hence, a natural and practical problem is the one of constructing greedy drawings in the plane using few bits for representing vertex Cartesian coordinates and using the Euclidean distance as a metric. We show that there exist greedy-drawable graphs that do not admit any greedy drawing in which the Cartesian coordinates have less than a polynomial number of bits.