Active Topology Inference using Network Coding

Our goal is to infer the topology of a network when (i) we can send probes between sources and receivers at the edge of the network and (ii) intermediate nodes can perform simple network coding operations, i.e., additions. Our key intuition is that network coding introduces topology-dependent correlation in the observations at the receivers, which can be exploited to infer the topology. For undirected tree topologies, we design hierarchical clustering algorithms, building on our prior work. For directed acyclic graphs (DAGs), first we decompose the topology into a number of two-source, two-receiver (2-by-2) subnetwork components and then we merge these components to reconstruct the topology. Our approach for DAGs builds on prior work on tomography, and improves upon it by employing network coding to accurately distinguish among all different 2-by-2 components. We evaluate our algorithms through simulation of a number of realistic topologies and compare them to active tomographic techniques without network coding. We also make connections between our approach and alternatives, including passive inference, traceroute, and packet marking

Active topology inference using network coding

Our goal, in this paper, is to infer the topology of a network when (i) we can send probes between sources and receivers at the edge of the network and (ii) intermediate nodes can perform simple network coding operations, i.e., additions. Our key intuition is that network coding introduces topology-dependent correlation in the observations at the receivers, which can be exploited to infer the topology. For undirected tree topologies, we design hierarchical clustering algorithms, building on our prior work in [24]. For directed acyclic graphs (DAGs), first we decompose the topology into a number of two source, two receiver (2-by-2) subnetwork components and then we merge these components to reconstruct the topology. Our approach for DAGs builds on prior work on tomography [36], and improves upon it by employing network coding to accurately distinguish among all different 2-by-2 components. We evaluate our algorithms through simulation of a number of realistic topologies and compare them to active tomographic techniques without network coding. We also make connections between our approach and other alternatives, including passive inference, traceroute, and packet marking

Active Learning of Multiple Source Multiple Destination Topologies

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 end-to-end 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 bottom-up 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 $N-1$ 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 near-optimal, but REA is more efficient in practice

A Network Coding Approach to Loss Tomography

Network tomography aims at inferring internal network characteristics based on measurements at the edge of the network. In loss tomography, in particular, the characteristic of interest is the loss rate of individual links and multicast and/or unicast end-to-end probes are typically used. Independently, recent advances in network coding have shown that there are advantages from allowing intermediate nodes to process and combine, in addition to just forward, packets. In this paper, we study the problem of loss tomography in networks with network coding capabilities. We design a framework for estimating link loss rates, which leverages network coding capabilities, and we show that it improves several aspects of tomography including the identifiability of links, the trade-off between estimation accuracy and bandwidth efficiency, and the complexity of probe path selection. We discuss the cases of inferring link loss rates in a tree topology and in a general topology. In the latter case, the benefits of our approach are even more pronounced compared to standard techniques, but we also face novel challenges, such as dealing with cycles and multiple paths between sources and receivers. Overall, this work makes the connection between active network tomography and network coding

Network monitoring in multicast networks using network coding

In this paper we show how information contained in robust network codes can be used for passive inference of possible locations of link failures or losses in a network. For distributed randomized network coding, we bound the probability of being able to distinguish among a given set of failure events, and give some experimental results for one and two link failures in randomly generated networks. We also bound the required field size and complexity for designing a robust network code that distinguishes among a given set of failure events