## Section: New Results

### Algorithms to Infer Topologies

Participants : Youssef Azzana, Fabrice Guillemin, Philippe Robert.

The inference of the Internet topology is highly relevant in studying the spread of attacks and malicious programs such as worms and DOS through the network. It helps also to change the routing in order to balance the load and troubleshoot operational problems and also for network management. Recently, many protocols like multicast applications, traffic matrix estimation rely on the knowledge of the network topology to optimize the service provision and to increase the quality of service perceived by end users.

One popular approach to discover the network topology consists in using the theory of random graphs (Erdos and Renyi graphs, small world). It permits the construction of a random graph based on some local properties. Indeed, it has been observed that the degree distribution obeys to a power law. However, it is worth noting that a small error for example in the estimation of the power law parameter due to incomplete data may lead to erroneous interpretations. Another method exploits the BGP messages exchanged by different AS (Autonomous Systems). Thus, it is possible to construct the AS graph simply by listening to BGP messages. Then, one can refine the graph by looking for the IGP messages also. The most widely used method is the traceroute probing. In this approach the network is considered like a black box which is gradually explored. Traceroutes between two different hosts allows the discovery of the whole routers along the path between them. Indeed, the source transmitting the traceroute message gradually increment the TTL field of the packets sent to the destination (the number of hopes traversed) which make it possible to obtain the list of intermediate routers. Practically, a certain number of machines considered as sources proceeds by executing traceroutes to a list of destinations and the results are merged to construct the global map of the Internet.

The results obtained last year have be extended to the case where the tree structure of the topology is not anymore regular and deterministic but is a Galton-Watson tree. If Fis the number of leaves of a node, several cases have been separately investigated when or when and , or finally when .