Abishek Gopalan

On identifying additive link metrics using linearly independent cycles and paths

In this paper, we study the problem of identifying constant additive link metrics using linearly independent monitoring cycles and paths. A monitoring cycle starts and ends at the same monitoring station, while a monitoring path starts and ends at distinct monitoring stations. We show that three-edge connectivity is a necessary and sufficient condition to identify link metrics using one monitoring station and employing monitoring cycles. We develop a polynomial-time algorithm to compute the set of linearly independent cycles. For networks that are less than three-edge-connected, we show how the minimum number of monitors required and their placement may be computed. For networks with symmetric directed links, we show the relationship between the number of monitors employed, the number of directed links for which metric is known a priori, and the identifiability for the remaining links. To the best of our knowledge, this is the first work that derives the necessary and sufficient conditions on the network topology for identifying additive link metrics and develops a polynomial-time algorithm to compute linearly independent cycles and paths.

On the maximum number of linearly independent cycles and paths in a network

Central to network tomography is the problem of identifiability, the ability to identify internal network characteristics uniquely from end-to-end measurements. This problem is often underconstrained even when internal network characteristics such as link delays are modeled as additive constants. While it is known that the network topology can play a role in determining the extent of identifiability, there is a lack in the fundamental understanding of being able to quantify it for a given network. In this paper, we consider the problem of identifying additive link metrics in an arbitrary undirected network using measurement nodes and establishing paths/cycles between them. For a given placement of measurement nodes, we define and derive the “link rank” of the network-the maximum number of linearly independent cycles/paths that may be established between the measurement nodes. We achieve this in linear time. The link rank helps quantify the exact extent of identifiability in a network. We also develop a quadratic time algorithm to compute a set of cycles/paths that achieves the maximum rank.

Multipath routing and dual link failure recovery in IP networks using three link-independent trees

We develop an approach for disjoint multipath routing and fast recovery in IP networks that guarantees recovery from arbitrary two link failures. We employ three link-independent trees, referred to as red, blue, and green trees, rooted at every destination. The path from a source to the destination on the trees are mutually link-disjoint. The routing of packets is based on the destination address and the input interface over which the packet was received. We discuss different ways of employing the three link-independent trees for multipath routing and/or failure recovery. If the trees are employed exclusively for multipath routing, then no packet overhead is required. If the trees are employed for failure recovery, then the overhead bits will range from 0 to 2 bits depending on the flexibility sought in routing. We evaluate the performance of the trees in fast recovery by comparing the path lengths provided under single and dual link failures with an earlier approach based on tunneling.

IP Fast Rerouting for Multi-Link Failures

IP fast reroute methods are used to recover packets in the data plane upon link failures. Previous work provided methods that guarantee failure recovery from at most two-link failures. We develop an IP fast reroute method that employs rooted arc-disjoint spanning trees to guarantee recovery from up to (k-1) link failures in a k-edge-connected network. As arc-disjoint spanning trees may be constructed in sub-quadratic time in the size of the network, our approach offers excellent scalability. Through experimental results, we show that employing arc-disjoint spanning trees to recover from multiple failures reduces path stretch in comparison with previously known techniques.

A counterexample for the proof of implication conjecture on independent spanning trees

Khuller and Schieber (1992) in [1] developed a constructive algorithm to prove that the existence of k-vertex independent trees in a k-vertex connected graph implies the existence of k-edge independent trees in a k-edge connected graph. In this paper, we show a counterexample where their algorithm fails.

Fast Recovery From Link Failures in Ethernet Networks

Fast-recovery from link failures is a well-studied topic in IP networks. Employing fast-recovery in Ethernet networks is complicated as the forwarding is based on destination MAC addresses, which do not have the hierarchical nature similar to those exhibited in Layer 3 in the form of IP-prefixes. Moreover, switches employ backward learning to populate the forwarding table entries. Thus, any fast recovery mechanism in Ethernet networks must be based on undirected spanning trees if backward learning is to be retained. In this paper, we develop three alternatives for achieving fast recovery from single link failures in Ethernet networks. All three approaches provide guaranteed recovery from single link failures. The approaches differ in the technologies required for achieving fast recovery, namely VLAN rewrite and/or mac-in-mac encapsulation. We study the performance of the approaches developed on five different networks.

IP fast rerouting and disjoint multipath routing with three edge-independent spanning trees

We develop approaches for disjoint multipath routing and fast recovery in IP networks that guarantee recovery from arbitrary two link failures. We achieve this by developing the first known algorithm to construct three edge-independent spanning trees, which has a running time complexity of O(V2). The property of these trees is that the paths from a source to the destination on the trees are mutually link-disjoint. We illustrate how the three edge-independent trees rooted at a destination may be employed to achieve multipath routing and IP fast recovery. We discuss different ways of employing the trees. The routing of packets is based on the destination address and the input interface over which the packet was received. If the trees are employed exclusively for multipath routing, then no packet overhead is required. If the trees are employed for failure recovery, then the overhead bits will range from 0 to 2 bits depending on the flexibility sought in routing. We evaluate the performance of the trees in fast recovery by comparing the path lengths provided under single- and dual-link failures with an earlier approach based on tunneling. We also evaluate the performance of the trees when used for multipath routing and compare it to equal-cost multipaths (ECMP).

On the Extraction and Analysis of a Social Network with Partial Organizational Observation

The behavior of an organization may be inferred based on the behavior of its members, their contacts, and their connectivity. One approach to organizational analysis is the construction and interpretation of a social network graph, where entities of an organization (persons, vehicles, locations, events, etc.) are nodes, and edges represent varying kinds of connectivity between entities. This paper describes a transformation based approach to the extraction of a social network graph, where the original data comprising (partial) observation of the organization are embedded on a graph with a different ontology, and with many entities and edges that are unrelated to the organization of interest. Social network extraction allows the inference of implied relationships, and the selection of relationships relevant for intended analysis techniques. The analysis of the resulting social network graph is based on organizational and individual analysis, in order to permit an advanced user to draw conclusions regarding the behavior of the organization, based on established social network graph metrics. The results of the paper include a discussion of the complexity of analysis, and how the observation data graph is pruned in order to scale the application of analysis algorithms.

Benefits of inter-flow bandwidth sharing in broadband wireless infrastructure networks

Broadband wireless infrastructure networks are increasingly becoming common in metro areas. To improve spatial bandwidth usage, the nodes in such networks employ directional transmissions over multiple orthogonal channels. In this paper, we study the benefits of sharing channel bandwidth across multiple flows. Every connection is assumed to require a bandwidth that is half of the channel bandwidth. We model the routing and channel assignment problem in two different ways to account for the presence and absence of inter-flow bandwidth sharing. Through simulations, we demonstrate that supporting inter-flow bandwidth sharing through simple time-sharing mechanism results in improved network throughput.