Load balancing by network curvature control

International Journal of Computers, Communications and Control

Volumn 6, Issue 1, 2011, Pages 134-149

  Lou, M ^a   Jonckheere, E ^b   Bonahon, F ^b   Baryshnikov, Y ^c   Krishnamachari, B ^b  

^a WESTERN DIGITAL CORPORATION   (United States)

^b UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

^c NOKIA RESEARCH CENTER   (United States)

Author keywords

Curvature; Gromov hyperbolic graphs; Inertia; Load balancing; Network congestion; Poincar disk; Yamabe flow

Indexed keywords

EID: 78649921098     PISSN: 18419836     EISSN: 18419844     Source Type: Journal    
DOI: 10.15837/ijccc.2011.1.2208     Document Type: Article

References (17)

1. F. Ariaei and E. Jonckheere, Cooperative 'curvature-driven' control of mobile autonomous sensor agent network, IEEE Conference on Decision and Control, New Orleans, LA, December 2007, pp. 1453-1458.
2. Y. Baryshnikov, On the curvature of the Internet, in Workshop on Stochastic Geometry and Teletraffic, Eindhoven, The Netherlands, April 2002.
3. L. M. Blumenthal, Theory and Applications of Distance Geometry, Oxford at the Clarendon Press, London, 1953.
4. M. Boguna, F. Papadopoulos and D. Krioukov, Sustaining the Internet with hyperbolic mapping, Nature Communications, volume 1, article number 62, September 2010.
5. M. Bonk and O. Schramm, Embeddings of Gromov hyperbolic spaces, Geom. Funct. Analysis, volume 10, pp. 266-306, 2000.
6. D. Burago, Y. Burago, and S. Ivanov, A Course in Metric Geometry, volume 33 of Graduate Study in Mathematics, American Mathematical Society, Providence, Rhode Island, 2001.
7. Cisco, How Does Load Balancing Work? Cisco Document ID: 5212,2005. http://www.cisco.com/en/US/tech/tk365/technologies_tech_note09186a0080094820.shtml.
8. E. Ghys and P. de la Harpe, editors. Sur les groupes hyperboliques d'après Mikhael Gromov, Number 83 in Progress in Mathematics, Birkhauser, Boston, MA, 1990. (Papers from the Swiss Seminar on Hyperbolic Groups held in Bern, 1988.)
9. M. Gromov, Hyperbolic groups, in S. M. Gersten, editor, Essays in Group Theory, volume 8 of Mathematical Sciences Research Institute Publication, pages 75-263, Springer-Verlag, New York, 1987.
10. M. Gromov, Metric Structures for Riemannian and Non-Riemannian Spaces, volume 152 of Progress in Mathematics, Springer-Verlag, 1999.
11. S. D. Fisher, Function Theory on Planar Domains: A Second Course in Complex Analysis, John Wiley & Sons, New York, 1983.
12. J. Jost, Nonpositive Curvature: Geometric and Analytic Aspects, Birkhauser, Lectures in Mathematics, Basel-Boston-Berlin, 1997.
13. J. Jost, Riemannian Geometry and Geometric Analysis, Second Edition, Springer, Universitext, Berlin, Heidelberg, New York, 1998.
14. M. Lou and E. A. Jonckheere, Tracking and mitigating piracy, American Control Conference, Minneapolis, MN, June 14-16, 2006, paper WeA20.2, Session: Networks and Control, pp. 656-661.
15. M. Lou, Traffic pattern analysis in negatively curved network, Ph.D. dissertation, Department of Electrical Engineering, University of Southern California, Los Angeles, Calif, USA, 2008.
16. F. Luo, Combinatorial Yamabe flow on surfaces, Communications in Contemporary Mathematics, volume 6, number 5, pp. 765-780, 2004.
17. L. Sun and X. Yu, Positively curved cubic plane graphs are finite, Journal of Graph Theory, volume 47, number 4, pp. 241-274, 2004.