Graph Algorithms for Network Tomography and Fault Tolerance

Abstract

The massive growth and proliferation of media, content, and services on the Internet are driving the need for more network capacity as well as larger networks. With increasing bandwidth and transmission speeds, even small disruptions in service can result in a significant loss of data. Thus, it is becoming increasingly important to monitor networks for their performance and to be able to handle failures effectively. Doing so is beneficial from a network design perspective as well as in being able to provide a richer experience to the users of such networks. Network tomography refers to inference problems in large-scale networks wherein it is of interest to infer individual characteristics, such as link delays, through aggregate measurements, such as end-to-end path delays. In this dissertation, we establish a fundamental theory for a class of network tomography problems in which the link metrics of a network are modeled to be additive. We establish the necessary and sufficient conditions on the network topology, provide polynomial time graph algorithms that quantify the extent of identifiability, and algorithms to identify the unknown link metrics. We develop algorithms for all graph topologies classified on the basis of their connectivity. The solutions developed in this dissertation extend beyond networking and are applicable in areas such as nano-electronics and power systems. We then develop graph algorithms to handle link failures effectively and to provide multipath routing capabilities in IP as well as Ethernet based networks. Our schemes guarantee recovery and are designed to pre-compute alternate next hops that can be taken upon link failures. This allows for fast re-routing as we avoid the need to wait for (control plane) re-computations.