Skip to main content
SpringerLink
Log in

Discrete Ricci Flow for Geometric Routing

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

Years and Authors of Summarized Original Work

  • 2009; Sarkar, Yin, Gao, Luo, Gu

  • 2010; Sarkar, Zeng, Gao, Gu

  • 2010; Zeng, Sarkar, Luo, Gu, Gao

  • 2011; Jiang, Ban, Goswami, Zeng, Gao, Gu

  • 2011; Yu, Ban, Sarkar, Zeng, Gu, Gao

  • 2012; Yu, Yin, Han, Gao, Gu

  • 2013; Ban, Goswami, Zeng, Gu, Gao

  • 2013; Li, Zeng, Zhou, Gu, Gao

Problem Definition

The problem is concerned about computing virtual coordinates for greedy routing in a wireless ad hoc network. Consider a set of wireless nodes S densely deployed inside a geometric domain \(\mathcal{R}\subseteq \mathbb{R}^{2}\). Nodes within communication range can directly communicate with each other. We ask whether one can compute a set of virtual coordinates for S such that greedy routing has guaranteed delivery. In particular, each node forwards the message to the neighbor whose distance to the destination, computed under the virtual coordinates and some metric function d, is the smallest. If such a neighbor can always be found, greedy routing successfully...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 1,599.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 1,999.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Recommended Reading

  1. Ban X, Goswami M, Zeng W, Gu XD, Gao J (2013) Topology dependent space filling curves for sensor networks and applications. In: Proceedings of 32nd annual IEEE conference on computer communications (INFOCOM’13), Turin

    Google Scholar 

  2. Chow B, Luo F (2003) Combinatorial Ricci flows on surfaces. J Differ Geom 63(1):97–129

    MathSciNet  MATH  Google Scholar 

  3. Goswami M, Ni C-C, Ban X, Gao J, Xianfeng Gu D, Pingali V (2014) Load balanced short path routing in large-scale wireless networks using area-preserving maps. In: Proceedings of the 15th ACM international symposium on mobile ad hoc networking and computing (Mobihoc’14), Philadelphia, Aug 2014. pp 63–72

    Google Scholar 

  4. Gu X, Luo F, Sun J, Wu T (2013) A discrete uniformization theorem for polyhedral surfaces. arXiv:13094175

    Google Scholar 

  5. Gu X, Guo R, Luo F, Sun J, Wu T (2014) A discrete uniformization theorem for polyhedral surfaces ii. arXiv:14014594

    Google Scholar 

  6. Jiang R, Ban X, Goswami M, Zeng W, Gao J, Gu XD (2011) Exploration of path space using sensor network geometry. In: Proceedings of the 10th international symposium on information processing in sensor networks (IPSN’11), Chicago, pp 49–60

    Google Scholar 

  7. Li S, Zeng W, Zhou D, Gu XD, Gao J (2013) Compact conformal map for greedy routing in wireless mobile sensor networks. In: Proceedings of 32nd annual IEEE conference on computer communications (INFOCOM’13), Turin

    Google Scholar 

  8. Sarkar R, Yin X, Gao J, Luo F, Gu XD (2009) Greedy routing with guaranteed delivery using Ricci flows. In: Proceedings of the 8th international symposium on information processing in sensor networks (IPSN’09), San Francisco, pp 97–108

    Google Scholar 

  9. Sarkar R, Zeng W, Gao J, Gu XD (2010) Covering space for in-network sensor data storage. In: Proceedings of the 9th international symposium on information processing in sensor networks (IPSN’10), Stockholm, pp 232–243

    Google Scholar 

  10. Stephenson K (2005) Introduction to circle packing: the theory of discrete analytic functions. Cambridge University Press, New York

    MATH  Google Scholar 

  11. Thurston WP (1997) Three-dimensional geometry and topology, vol 1. Princeton University Press, Princeton

    MATH  Google Scholar 

  12. Yu X, Yin X, Han W, Gao J, Gu XD (2012) Scalable routing in 3d high genus sensor networks using graph embedding. In: Proceedings of the 31st annual IEEE conference on computer communications (INFOCOM’12), Orlando, pp 2681–2685

    Google Scholar 

  13. Zeng W, Sarkar R, Luo F, Gu XD, Gao J (2010) Resilient routing for sensor networks using hyperbolic embedding of universal covering space. In: Proceedings of the 29th annual IEEE conference on computer communications (INFOCOM’10), San Diego, pp 1694–1702

    Google Scholar 

  14. Zhang M, Guo R, Zeng W, Luo F, Yau ST, Gu X (2014) The unified discrete surface Ricci flow. Graph Models. doi:. http://www.sciencedirect.com/science/article/pii/S1524070314000344

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Stony Brook University, 11794, Stony Brook, NY, USA

    Jie Gao

  2. Department of Computer Science, Stony Brook University, 11794, Stony Brook, NY, USA

    Xianfeng David Gu

  3. Department of Mathematics, Rutgers University, Piscataway, NJ, USA

    Feng Luo

Authors
  1. Jie Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xianfeng David Gu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Feng Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jie Gao .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer Science+Business Media New York

About this entry

Cite this entry

Gao, J., David Gu, X., Luo, F. (2016). Discrete Ricci Flow for Geometric Routing. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_602

Download citation

Publish with us

Policies and ethics

Search

Navigation