Some Results on Greedy Embeddings in Metric Spaces

Authors:
Tom Leighton;Ankur Moitra
Affiliations:
Massachusetts Institute of Technology, Math. Department and CSAIL, 02139, Cambridge, MA, USA;Massachusetts Institute of Technology, EECS Department and CSAIL, 02139, Cambridge, MA, USA
Venue:
Discrete & Computational Geometry
Year:
2010

Citing 0
Cited 8

Competitive routing in the half-θ6-graph

Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Monotone drawings of graphs with fixed embedding

GD'11 Proceedings of the 19th international conference on Graph Drawing
Succinct greedy drawings do not always exist

Networks
Succinct strictly convex greedy drawing of 3-connected plane graphs

FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
Space lower bounds for low-stretch greedy embeddings

SIROCCO'12 Proceedings of the 19th international conference on Structural Information and Communication Complexity
Self-approaching graphs

GD'12 Proceedings of the 20th international conference on Graph Drawing
A simple routing algorithm based on Schnyder coordinates

Theoretical Computer Science
Category-based routing in social networks: Membership dimension and the small-world phenomenon

Theoretical Computer Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

Geographic Routing is a family of routing algorithms that uses geographic point locations as addresses for the purposes of routing. Such routing algorithms have proven to be both simple to implement and heuristically effective when applied to wireless sensor networks. Greedy Routing is a natural abstraction of this model in which nodes are assigned virtual coordinates in a metric space, and these coordinates are used to perform point-to-point routing. Here we resolve a conjecture of Papadimitriou and Ratajczak that every 3-connected planar graph admits a greedy embedding into the Euclidean plane. This immediately implies that all 3-connected graphs that exclude K 3,3 as a minor admit a greedy embedding into the Euclidean plane. We also prove a combinatorial condition that guarantees nonembeddability. We use this result to construct graphs that can be greedily embedded into the Euclidean plane, but for which no spanning tree admits such an embedding.