Brief announcement

摘要

A widely used mechanism for computing the topology of any network in the Internet is Traceroute. Using Traceroute, one simply needs to choose any two nodes in a network and then obtain the sequence of nodes that occur between these two nodes, as specified by the routing tables in these nodes. Thus, each use of Traceroute in a network produces a trace of nodes that constitute a simple path in this network. In every trace that is produced by Traceroute, each node occurs either by its unique identifier or by the anonymous identifier "*". In this paper, we introduce the first theory aimed at answering the following important question. Is there an algorithm to compute the topology of a network N from a trace set T that is produced by using Traceroute in N, assuming that each edge in N occurs in at least one trace in T, and that each node in N occurs by its unique identifier in at least one trace in T? Our theory shows that the answer to this questionis "No" in general. But if N is a tree, or is an odd ring, then the answer is "Yes". On the other hand, if N is an even ring, the answer is "No", but if N is a "mostly regular" even ring, then the answer is "Yes".