Graphs & digraphs (2nd ed.)
Introduction to algorithms
A random graph model for massive graphs
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
On the covariance of the level sizes in random recursive trees
Random Structures & Algorithms
On the Spectrum and Structure of Internet Topology Graphs
IICS '02 Proceedings of the Second International Workshop on Innovative Internet Computing Systems
Should we build Gnutella on a structured overlay?
ACM SIGCOMM Computer Communication Review
FIRST-PASSAGE PERCOLATION ON THE RANDOM GRAPH
Probability in the Engineering and Informational Sciences
A survey of peer-to-peer content distribution technologies
ACM Computing Surveys (CSUR)
On the bias of traceroute sampling: or, power-law degree distributions in regular graphs
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Performance Analysis of Communications Networks and Systems
Performance Analysis of Communications Networks and Systems
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
On properties of multicast routing trees: Research Articles
International Journal of Communication Systems
Data Communications Networking
Data Communications Networking
Implications for QoS provisioning based on traceroute measurements
QofIS'02/ICQT'02 Proceedings of the 3rd international conference on quality of future internet services and internet charging and QoS technologies 2nd international conference on From QoS provisioning to QoS charging
Sampling networks by the union of m shortest path trees
Computer Networks: The International Journal of Computer and Telecommunications Networking
| Hi-index | 0.00 |
The union of all shortest path trees GUspt is the maximally observable part of a network when traffic follows shortest paths. Overlay networks such as peer to peer networks or virtual private networks can be regarded as a subgraph of GUspt. We investigate properties of GUspt in different underlying topologies with regular i.i.d. link weights. In particular, we show that the overlay GUspt in an Erdös-Rényi random graph Gp (N) is a connected GPc (N) where Pc ∼ log N/N is the critical link density, an observation with potential for ad-hoc networks. Shortest paths and, thus also the overlay GUspt, can be controlled by link weights. By tuning the power exponent α of polynomial link weights in different underlying graphs, the phase transitions in the structure of GUspt are shown by simulations to follow a same universal curve FT (α) = Pr[GUspt is a tree]. The existence of a controllable phase transition in networks may allow network operators to steer and balance flows in their network. The structure of GUspt in terms of the extreme value index α is further examined together with its spectrum, the eigenvalues of the corresponding adjacency matrix of GUspt.