Pierre Fraigniaud

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Consider a team of mobile software agents deployed to capture a (possibly hostile) intruder in a network. All agents, including the intruder move along the network links; the intruder could be arbitrarily fast, and aware of the positions of all the agents. The problem is to design the agents' strategy for capturing the intruder. The main efficiency(More)
Several papers showed how to perform routing in <i>ad hoc</i> wireless networks based on the positions of the mobile hosts. However, all these protocols are likely to fail if the transmission ranges of the mobile hosts vary due to natural or man-made obstacles or weather conditions. These protocols may fail because in routing either some connections are not(More)
This paper is a survey of existing methods of communication in usual networks. We particularly study the complete network, the ring, the torus, the grid, the hypercube, the cube connected cycles, the undirected de Bruijn graph, the star graph, the shuffle-exchange graph, and the butterfly graph. Two different models of communication time are analysed,(More)
An n-node tree has to be explored by k mobile agents (robots), starting in its root. Every edge of the tree must be traversed by at least one robot, and exploration must be completed as fast as possible. Even when the tree is known in advance, scheduling optimal collective exploration turns out to be NP-hard. We investigate the problem of distributed(More)
We consider small world graphs as defined by Kleinberg (2000), i.e., graphs obtained from a <i>d</i>-dimensional mesh by adding links chosen at random according to the <i>d</i>-harmonic distribution. This model aims at giving formal support to the "six degrees of separation" between individuals experienced by Milgram (1967),and verified recently by Dodds,(More)