Lecture Notes in Computer Science Volume 5849, 2010, pp 171-182

Succinct Greedy Drawings Do Not Always Exist

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Abstract

A greedy drawing is a graph drawing containing a distance-decreasing path for every pair of nodes. A path (v 0,v 1,...,v m ) is distance-decreasing if d(v i ,v m ) < d(v i − 1,v m ), 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.

This work is partially supported by the Italian Ministry of Research, Grant number RBIP06BZW8, FIRB project “Advanced tracking system in intermodal freight transportation”.