Francis Bonahon

Publications (2)0 Total impact

• Source

  Available from: univagora.ro

  Article: Load Balancing by Network Curvature Control

  M Lou, E Jonckheere, F Bonahon, Y Baryshnikov, B Krishnamachari, Edmond Jonckheere, Francis Bonahon, Bhaskar Krishnamachari, Yuliy Baryshnikov
  [show abstract] [hide abstract]
  ABSTRACT: The traditional heavy-tailed interpretation of congestion is chal-lenged in this paper. A counter example shows that a network with uniform degree can have significant traffic congestion when the degree is larger than 6. A profound understanding of what causes congestion is reestablished, based on the network curvature theorem. A load balancing algorithm based on curvature control is presented with network applications.
  Int. J. of Computers. 04/2011; VI:134-149.
• Source

  Available from: ArXiv

  Article: Euclidean versus hyperbolic congestion in idealized versus experimental networks

  Edmond Jonckheere, Mingji Lou, Francis Bonahon, Yuliy Baryshnikov
  [show abstract] [hide abstract]
  ABSTRACT: This paper proposes a mathematical justification of the phenomenon of extreme congestion at a very limited number of nodes in very large networks. It is argued that this phenomenon occurs as a combination of the negative curvature property of the network together with minimum length routing. More specifically, it is shown that, in a large n-dimensional hyperbolic ball B of radius R viewed as a roughly similar model of a Gromov hyperbolic network, the proportion of traffic paths transiting through a small ball near the center is independent of the radius R whereas, in a Euclidean ball, the same proportion scales as 1/R^{n-1}. This discrepancy persists for the traffic load, which at the center of the hyperbolic ball scales as the square of the volume, whereas the same traffic load scales as the volume to the power (n+1)/n in the Euclidean ball. This provides a theoretical justification of the experimental exponent discrepancy observed by Narayan and Saniee between traffic loads in Gromov-hyperbolic networks from the Rocketfuel data base and synthetic Euclidean lattice networks. It is further conjectured that for networks that do not enjoy the obvious symmetry of hyperbolic and Euclidean balls, the point of maximum traffic is near the center of mass of the network. Comment: 23 pages, 4 figures
  11/2009;