On the Discovery of Random Trees

Abstract. We consider in this paper the problem of discovering, via a traceroute algorithm, the topology of a network, whose graph is spanned by an infinite branching process. A subset of nodes is selected according to some criterion. The minimal sub-tree containing the selected nodes is the set of those nodes discovered by the algorithm. For the selection of nodes, two criteria are considered: A node is randomly selected with a probability, which is either independent of the depth of the node (uniform model) or else in the depth biased model, is exponentially decaying with respect to its depth. The limiting behavior the size of the discovered subtree is investigated for both models. Contents

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Fabrice Guillemin, Philippe Robert
• Keywords: CORR 2007, Education, Infinite Branching Process, Minimal Sub-tree, Traceroute Algorithm