Succinct greedy drawings do not always exist

Abstract

AbstractA 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. © 2012 Wiley Periodicals, Inc. NETWORKS, 2012