# Encyclopedia of Algorithms

Editors: Ming-Yang Kao

# Routing in Geometric Networks

• Stephane Durocher
• Leszek Gasieniec
• Prudence W. H. Wong
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-2864-4_352

## Synonyms

Geographic routing; Location-based routing

## Years and Authors of Summarized Original Work

• 1999; Kranakis, Singh, Urrutia

• 1999; Bose, Morin, Stojmenovic, Urrutia

• 2003; Kuhn, Wattenhofer, Zhang, Zollinger

## Problem Definition

Wireless networks are often modelled using geometric graphs. Using only local geometric information to compute a sequence of distributed forwarding decisions that send a message to its destination, routing algorithms can succeed on several common classes of geometric graphs. These graphs’ geometric properties provide navigational cues that allow routing to succeed using only limited local information at each node.

### Network Model

A common geometric graph model for wireless networks is to represent each node by a point in the Euclidean plane, $$\mathcal{R}^{2}$$

### Keywords

Face routing Geometric routing Unit disk graph Wireless communication
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1. 1.
Bose P, Morin P, Stojmenovic I, Urrutia J (1999) Routing with guaranteed delivery in ad hoc wireless networks. In: Proceedings of the third international workshop on discrete algorithm and methods for mobility, Seattle, Aug 1999, pp 48–55
2. 2.
Bose P, Brodnik A, Carlsson S, Demaine ED, Fleischer R, López-Ortiz A, Morin P, Munro I (2002) Online routing in convex subdivisions. Int J Comput Geom Appl 12(4):283–295
3. 3.
Bose P, Carmi P, Durocher S (2013) Bounding the locality of distributed routing algorithms. Distrib Comput 26(1):39–58
4. 4.
Bose P, Durocher S, Mondal D, Peabody M, Skala M, Wahid MA (2015) Local routing in convex subdivisions. In: Proceedings of the forty-first international conference on current trends in theory and practice of computer science, Pec pod Sněžkou, Jan 2015, vol 8939, pp 140–151Google Scholar
5. 5.
Braverman M (2008) On ad hoc routing with guaranteed delivery. In: Proceedings of the twenty-seventh ACM symposium on principles of distributed computing, Toronto, vol 27, p 418Google Scholar
6. 6.
Durocher S, Kirkpatrick DG, Narayanan L (2010) On routing with guaranteed delivery in three-dimensional ad hoc wireless networks. Wirel Netw 16(1):227–235
7. 7.
Kranakis E, Singh H, Urrutia J (1999) Compass routing on geometric networks. In: Proceedings of the eleventh Canadian conference on computational geometry, Vancouver, Aug 1999, pp 51–54Google Scholar
8. 8.
Kuhn F, Wattenhofer R, Zollinger A (2002) Asymptotically optimal geometric mobile ad-hoc routing. In: Proceedings of the sixth international workshop on discrete algorithm and methods for mobility, Atlanta, Sept 2002, pp 24–33Google Scholar
9. 9.
Kuhn F, Wattenhofer R, Zhang Y, Zollinger A (2003) Geometric ad-hoc routing: of theory and practice. In: Proceedings of the twenty-second ACM symposium on the principles of distributed computing, Boston, July 2003, pp 63–72

© Springer Science+Business Media New York 2016

## Authors and Affiliations

• Stephane Durocher
• 1
• Leszek Gasieniec
• 2
• Prudence W. H. Wong
• 3
1. 1.University of ManitobaWinnipegCanada
2. 2.University of LiverpoolLiverpoolUK
3. 3.University of LiverpoolLiverpoolUK