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Section: New Results

Network Algorithms and Analysis

Information dissemination on social networks

In [17] , we model an online social network as a network formation game. We study convergence of selfish dynamics and show that somewhat natural metric assumption enable fast convergence towards an equilibrium with efficient collaborative filtering of content.

Verification of network forwarding tables

In [25] , we investigate the problem of verifying forwarding network tables. We show that it is sufficient to test few representative headers when the set of rules applied by routers is complete under intersection.

Refreshing old datasets in a network: LiveRank

In [18] , we consider the problem of refreshing a dataset. More precisely, given a collection of nodes gathered at some time (Web pages, users from an online social network) along with some structure (hyperlinks, social relationships), we want to identify a significant fraction of the nodes that still exist at present time. The liveness of an old node can be tested through an online query at present time. We call LiveRank a ranking of the old pages so that active nodes are more likely to appear first. The quality of a LiveRank is measured by the number of queries necessary to identify a given fraction of the active nodes when using the LiveRank order. We study different scenarios from a static setting where the LiveRank is computed before any query is made, to dynamic settings where the LiveRank can be updated as queries are processed. Our results show that building on the PageRank can lead to efficient LiveRanks, for Web graphs as well as for online social networks.

Exploiting user movement for position detection

The major issue of indoor localization system is the trade-off between implementation cost and accuracy. A low-cost system which demands only few hardware devices could save the cost but often it turns out to be less reliable. Aiming at improving classical triangulation method that requires several reference points, we propose in [34] a new method, called Two-Step Movement (2SM), which requires only one reference point (RP) by exploiting useful information given by the position change of a mobile terminal (MT), or the user movement. This method can minimize the number of reference points required in a localization system or navigation service and reduce system implementation cost. Analytical result shows that the user position can be thus derived and given in simple closed-form expression. Finally, simulation is conducted to demonstrate its effectiveness under noisy environment.

Then, in [35] , we build on 2SM. We first improve the positioning performance through multi-sampling technique to combat measurement noise. Secondly, we propose the Generalized Two-Step Movement (G2SM) method for device-to-device (D2D) systems in which both the mobile terminal (MT) and RP can be mobile device. The mobile user's position can be derived analytically and given in simple closed-form expression. Its effectiveness in the presence of noise is shown in simulation results.

Fast diameter and radius computation in real-world graphs

In [5] , we propose a new algorithm that computes the radius and the diameter of a weakly connected digraph G=(V,E), by finding bounds through heuristics and improving them until they are validated. Although the worst-case running time is O(|V||E|), we will experimentally show that it performs much better in the case of real-world networks, finding the radius and diameter values after 10100 runs of Breadth First Search instead of |V| BFS-s (independently of the value of |V|), and thus having running time O(|E|) in practice. As far as we know, this is the first algorithm able to compute the diameter of weakly connected digraphs, apart from the naive algorithm, which runs in time Ω(|V||E|) performing a BFS from each node. In the particular cases of strongly connected directed or connected undirected graphs, we have compared our algorithm with known approaches by performing experiments on a dataset composed by several real-world networks of different kinds. These experiments show that, despite its generality, the new algorithm outperforms all previous methods, both in the radius and in the diameter computation, both in the directed and in the undirected case, both in average running time and in robustness. Finally, as an application example, we have used the new algorithm to determine the solvability over time of the “Six Degrees of Kevin Bacon” game, and of the “Six Degrees of Wikipedia” game. As a consequence, we have computed for the first time the exact value of the radius and the diameter of the whole Wikipedia digraph.