Active Learning of Multiple Source Multiple Destination Topologies
Abstract
We consider the problem of inferring the topology of a network with $M$ sources and $N$ receivers (hereafter referred to as an $M$by$N$ network), by sending probes between the sources and receivers. Prior work has shown that this problem can be decomposed into two parts: first, infer smaller subnetwork components (i.e., $1$by$N$'s or $2$by$2$'s) and then merge these components to identify the $M$by$N$ topology. In this paper, we focus on the second part, which had previously received less attention in the literature. In particular, we assume that a $1$by$N$ topology is given and that all $2$by$2$ components can be queried and learned using endtoend probes. The problem is which $2$by$2$'s to query and how to merge them with the given $1$by$N$, so as to exactly identify the $2$by$N$ topology, and optimize a number of performance metrics, including the number of queries (which directly translates into measurement bandwidth), time complexity, and memory usage. We provide a lower bound, $\lceil \frac{N}{2} \rceil$, on the number of $2$by$2$'s required by any active learning algorithm and propose two greedy algorithms. The first algorithm follows the framework of multiple hypothesis testing, in particular Generalized Binary Search (GBS), since our problem is one of active learning, from $2$by$2$ queries. The second algorithm is called the Receiver Elimination Algorithm (REA) and follows a bottomup approach: at every step, it selects two receivers, queries the corresponding $2$by$2$, and merges it with the given $1$by$N$; it requires exactly $N1$ steps, which is much less than all $\binom{N}{2}$ possible $2$by$2$'s. Simulation results over synthetic and realistic topologies demonstrate that both algorithms correctly identify the $2$by$N$ topology and are nearoptimal, but REA is more efficient in practice.
 Publication:

arXiv eprints
 Pub Date:
 December 2012
 arXiv:
 arXiv:1212.2310
 Bibcode:
 2012arXiv1212.2310S
 Keywords:

 Computer Science  Networking and Internet Architecture
 EPrint:
 IEEE Transactions on Signal Processing, Vol. 62, Issue 8, pp. 19261937, April 2014