Analysis of Steiner subtrees of Random Trees for Traceroute Algorithms

TL;DR

This paper analyzes how different node selection strategies affect the size of Steiner subtrees discovered by traceroute algorithms in infinite branching network models, providing insights into network topology discovery efficiency.

Contribution

It introduces a probabilistic framework for studying Steiner subtree sizes in infinite branching networks under uniform and depth-biased node selection models.

Findings

Size of discovered subtrees varies with selection criteria.

Depth-biased selection leads to different limiting behaviors.

Results inform efficient network topology discovery strategies.

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. As a measure of efficiency of the algorithm, the Steiner distance of the selected nodes, i.e. the size of the spanning sub-tree of these nodes, is investigated. 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.